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MicFFT v1.1 March 31, 1993 Written by Craig M. Walsh CIS 70701,1614 Internet: Walsh@biovx1.dnet.nasa.gov Walsh@129.97.26.1 Introduction: MicFFT is a program that samples data from a sound card or addressable analog-to-digital (ADC) port, and plots out the spectral features of the sampled waveform. The program utilizes a Fast Fourier Transform (FFT) algorithm to transform the sampled data (in the time domain) to the frequency domain. The program gets 256 Pulse Code Modulated (PCM-see below) samples from the ADC at a defined sampling rate, and then plots the transformed data. MicFFT continuously loops between sampling and plotting. Thus, the program acts somewhat like a realtime spectrum analyzer, and on fast machines with fast sound cards, is capable of impressive performance. MicFFT can be likened to spectrum analyzers found on some audio equalizers, and can provide detailed information on the spectral components and relative intensities of continuous waveforms. Improvements in version 1.1: Since many of you heeded my call for comments in the last version, I was able to gain insight into what improvements to include in this version of MicFFT. The main problem I found was that the original version of MicFFT did not support Sound Blaster or Sound Blaster-compatible cards, even though I presumed it might. After some investigation, I found that sampling on the SB card requires quite a bit of additional code that was not included in the original version of MicFFT. Since I don't have an SB card (I have a Covox Sound Master II, and am quite happy with it so far!), I had to find someone out there with one to help out. Fortunately, Chris Pye decided to join the MicFFT "development team", and has supplied the SB sampling routines (along with additional ideas, etc.) for this new version. Now, MicFFT v1.1 has explicit support for SB 8-bit cards (16 bit sampling is, sadly, not included yet). Additionally, other cards that have Sound Blaster compatibility should also work with MicFFT (see Compatibility); I hope this time I don't eat my words! MicFFT also has a new function that provides for freezing waveform sampling and allows detailed analysis of the frozen waveform. This function has a positionable cursor-line, which can be used to determine the frequency and amplitude of a specific band on the plot. The program also has a new plotting mode that allows plots to be generated in either bar graph style, as implemented in the original version, or line graph style, which produces output that may be more suitable to certain applications. Output is also scaled in decibel (dB) steps. Some new filtering options have been added to MicFFT v1.1; Squelch allows filtering of spurious noise below a set threshold; Cosine envelope is used to reduce transformation errors resulting from sampling discontinuities (see Cosine Envelope, below). In addition, certain bugs that were not identified before the original release have been fixed (I hope). Requirements: MicFFT is a computing-intensive program and requires a fast computer for achieving rapid output. It was developed on a 33MHz 486-DX (with floating-point coprocessor), with SVGA, a Covox SoundMaster II sound card. Graphics modes tested include both EGA and VGA, so both should work (see Options). MicFFT will look for a coprocessor (and will run much faster if one is found), but will emulate one if a coprocessor is found. Additionally, some 286-specific code is included for speed, and thus it will not work properly on machines with lesser processors. Since the sampling routine is timed and independent of the transformation and plotting, the speed of a particular machine should not affect the accuracy of frequency output; only the rate at which data is plotted will be affected. Supported Sound Cards: As stated above, this version of MicFFT explicitly supports the Covox SoundMaster II (default) and the Sound Blaster cards for 8-bit sampling. The Sound Blaster mode, which includes additional code for sending commands to control the sampling specifics, is available using the -B1 flag (see Options). Other cards may work as well, particularly if some means for Sound Blaster compatibility is provided by the card. For example, the Pro Audio Spectrum card may work if a Sound Blaster compatability driver for that card is loaded before running MicFFT. This has not been tested yet, but you should check out your sound card documentation for specifics. Covox compatibility (default) is likely not explicitly provided by other sound card vendors. However, it may be generally useful to those whose cards are capable of polling the ADC independently (without explicit commands for controlling sampling); MicFFT provides a means for changing the default ADC port address. In the Covox mode, MicFFT simply looks for data at this port at a defined rate using timing routines in the program. The default port address included in the program is 22F (hex). This is actually a port address (0x220h) and ADC offset (0x00F) added together. If you have a card where a port address is given in the documentation, and an ADC input offset is also given, just add the two together (using a hex calculator) and use the -P flag to let MicFFT know which address you need to use. I realize that this discussion may be a bit technical, but I provide it so that users with cards other than the above mentioned can attempt to figure out which options to alter. I know that incompatibility is frustrating, so if you have a card which is not explicitly supported (and there is really a growing list), I will include compatibility for such cards for those who can get me specific code for PCM sampling. I prefer to have short code segments (in C, or assembler if possible) to look at rather than libraries, since I need to be able to control some of the aspects of sampling, and I need you to volunteer for testing the modified code. Contact me at the address provided (see Contacting the Author), and I will happily discuss your specific needs. (It should be noted that I may decide to port MicFFT to Windows, if I can pull together some cash for buying a Windows C compiler. This would be helpful, since compatibility would not be an issue here.) Lesson 1. PCM sampling: Sampling is a process whereby a continuous stream of data is broken up into chunks of data usable by the sampling system. PCM sampling is a process whereby this continuous data is polled at a defined rate. Since we are interested in analog signals most of the time (the type that enter our sound cards via the ADC port), it is necessary to first transform the data from an analog representation to a digital one. This is the job of the ADC. This process is fairly complicated, but suffice it to say that an analog value (from - infinity to + infinity) is transformed to an explicit digital value. Since the digital value can represent only a discrete value, there may be some loss of resolution in this transformation. 16 bit cards (which can represent 64K different input levels) are much more accurate for this purpose than 8 bit cards (which only can reproduce 256 different levels). Also, since PCM-sampling assumes that the analog waveform has components on either side of zero (i.e. negative and positive parts of a wave), one half of the digital range is negative, the other half positive. This reduces the number of possible digital absolute value amplitudes by a factor of two, which affects the dynamic range (i.e. the lowest to highest amplitude) of a particular digital system. Digital conversion produces a sample value, and this is done at a discrete sampling frequency so that points of a continuous analog waveform are approximated by a set of digital values. These digital values can be stored into the computer's memory and played back to reproduce an approximation of the original analog waveform. The process of rebuilding an analog waveform from digital samples requires that the samples are "played back" at a rate similar to the rate at which the samples were originally obtained. To do this, each sample is transformed from a digital value to an analog value (using a digital-to- analog converter, or DAC) and this is done for all of the stored samples at the chosen sampling frequency. Thus, an approximation of the original analog waveform can be reproduced. The accuracy of sampling thus depends on two major variables: the sampling rate and the number of possible sample values. The sampling rate can affect accuracy since it defines the highest possible frequency from the original waveform that can be sampled. The Nyquist sampling theorem dictates that the sampling rate must be at least twice the frequency of the highest frequency component to be sampled. Thus, frequencies greater than one-half the sampling frequency (the Nyquist limit) will not be sampled accurately. Attempting to surpass this limit will introduce errors into the sampled waveform. To get around this limitation in practical sampling systems (e.g. digital Compact Disc recording and playback, etc.), engineers utilize low-pass filters which attenuate signals of frequencies higher than the Nyquist limit prior to digital sampling. For CDs, which have a sampling rate of 44.1 kHz, these low-pass filters begin attenuating at about 21 kHz and have reduced the signal at the Nyquist limit of 22.05 kHz almost entirely. Thus, a CD can have data sampled upto about 22 kHz, but no higher, and is thus "bandwidth-limited." Sampling any higher frequencies would create undesirable noise in the output. (Note that 44.1 kHz is chosen because it is about the lowest value for accurately sampling the spectrum of frequencies important in musical signals; about 15 Hz to 20 kHz. Any higher value would be unnecessary and would require an increase data storage, an obvious limitation for a system with two digital PCM channels and error-correction data included with the PCM data). The second limitation to accurate PCM sampling is related to the number of bits each sample contains. CD sampled material is 16- bit PCM. This corresponds to a dynamic range of about 96 decibels (dB). Systems using smaller sized samples will obviously have lower dynamic range. Thus, they will have an inherently higher level of noise, and are inappropriate for high-fidelity reproduction of sound. Of course, the tradeoff between sound quality and data storage is an important design consideration in any PCM system. Lesson 2. Superposition: It is fairly easy to figure out what a sinewave looks like from an oscilloscope plot. You've likely heard what a sinewave sounds like; pretty boring. A simple sinewave can produce a tone. However, most sound that we hear and find pleasing has much more content than a single sinewave. Musical instruments produce waveforms with a fundamental (do not confuse with my terminology below; fundamental here refers to the primary frequency created by an instrument) frequency (sinewave) and a group of harmonic sinewaves at multiples of the fundamental. These "harmonics" give each instrument a recognizable sound, or timbre. When we break up the waveform, it is possible to show that the original waveform is thus the addition of the fundamental sinewave and all of its harmonic sinewaves. This addition is called superposition. Of course, superposition can be both additive, or destructive. Destructive superposition can actually cancel out the amplitudes of two waveforms (for example, if both are of the same frequency and amplitude, but are 90 degrees out of phase; i.e. the peak of the first wave corresponds to the trough of the second). If you listen to two sinewaves being reproduced by the FM chip on your sound card (if you have one), you will be listening to superimposed sinewaves. However, since your ear is able to pull out the discrete frequencies in the signal, you hear two sinewaves (sort of like the FFT routine described below). Pretty neat, huh? Lesson 3. Fourier Transforms: Many of you may have seen programs that take PCM sampled sound and output the data on the screen in an oscilloscope-like display. In this case, the plot is based on amplitude vs. time. It is possible to determine the relative frequency of a continuous waveform by varying the sweep-rate of such an oscilloscope, but there are better ways to gather frequency data from PCM samples. One approach is to pass the data through an algorithm called a Fast Fourier Transform (FFT) and to plot the resulting data as a magnitude vs. frequency plot. Essentially, the FFT loops thru a group of samples and pulls out all of the sinewaves contained in the sampling period (delta). Since we know the sampling rate (and thus, the time between samples), it is possible to assign frequency values to the sinewaves determined by the FFT. So, the Fourier Transform works like the superposition principle in reverse. The first sinewave is the lowest possible sinewave that can be sampled accurately by the FFT, and corresponds to the sampling frequency divided by the number of samples in delta. I refer to this as the fundamental frequency of the plot, F-fund. The frequency band plotted is twice F-fund, and the next is 3X, and so on. Thus, the plotted bands continue up by multiples of F- fund until we reach the Nyquist limiting frequency (F-Ny), which incidentally has a band number equal to 1/2 the number of samples in delta (band number is also called channel number; one band is plotted for each frequency displayed by MicFFT for a particular sampling frequency). Generally, data is plotted in by linear scaling along the frequency axis, which means that each band plotted represents one frequency. However, it should be noted that frequencies located between two discrete bands will be represented as maximal deflections of the two bands on either side of this intervening frequency. Additionally, even band-centered frequencies will produce deflections of those bands adjacent to it, tapering off as we move in either direction from the center band. One should use care when ascribing a particular group of frequencies to a particular plot; as you work with MicFFT, you will get an idea of what to expect. MicFFT Usage: When you start MicFFT with the appropriate command line arguments (see Options), you will be able to begin sampling signals entering the ADC. Whistle into a microphone connected to the sound card. You should see a peak, corresponding to the frequency of the whistle. Since the whistle is produced at the lips, there is little interaction with the resonant cavities or the body that normally introduce harmonics in speech and singing. Thus, whistling approximates a sinewave and can be used to test MicFFT for simple waveforms. Vary the pitch of your whistling. By reducing the pitch, you should see this peak move to the left, thus indicating that the frequency is moving lower. By raising the pitch, the peak should move to the right of the plot (note that the degree of peak movement will be affected by the chosen sampling frequency). Note the ruler at the bottom of the plot screen. This ruler corresponds to the multiples of the fundamental frequency. Ones are in white, fives are in orange and tens are in red. You can use the ruler to get an instant idea of the relative frequency during sampling. It is now possible to freeze the plot by pressing the SPACE bar. Do this while continuing to whistle. Once the sampling has stopped and you have a frozen waveform frequency spectrum on the screen, you can use the arrow keys to move a cursor line around the plot. Move the cursor line to the peak. Below, you will see the frequency for this peak, as well as the amplitude (in magnitude returned by the FFT routine, and based on a maximum of 128; and in dB, relative to a dynamic range from 1 to 48 dB for the 8-bit samples). Note that the power density is related to the area under the peak; the magnitudes shown are plotted only for the band under the cursor line. Keys for Freeze Window: To move the cursor line around, use the LEFT or RIGHT keys for single band movements. To speed up movement around the plot, use CTRL-LEFT or CTRL-RIGHT to move ten bands for each keypress. To move to the right end of the plot, press END or PGDN; to move all the way to the left side, use HOME or PGUP. To return to the sampling mode, press the SPACE bar. To exit the program at any time (during sampling or in the freeze window), press ESC. Options: MicFFT v1.1 has a number of options which are set by command line arguments using specified flags. Typing MicFFT at the DOS prompt without any flags will run the program with the built-in defaults. You can override these defaults using the following flags: -?: Display command line options. Also -h. -f: Change the sampling frequency. -f25000 will change the sampling frequency to 25 kHz. Valid range is from 1 Hz (which would take 256 seconds before the first plot; not recommended...) and the highest sampling rate of your sound card. For the Covox card, this is 25000 (although I've been able to get upto 34090 Hz before getting sampling problems). For the Sound Blaster, this is 13 kHz. Play around with this option a lot. Default is 10000. -p: Change the default ADC port address. Default is 22F (hex), which corresponds to the default for the Covox card. -f24fh will change to port address/offset 24F. If you use the Sound Blaster mode (see -b flag), the default will be 220. Note that if you supply a hexidecimal address, use an "h" following the address to signify that you are using a hex address. Decimal addresses are assumed and require no h at the end. MicFFT will report the address chosen, so you can verify that the correct address has been selected. -b: Change the sound card mode. The default is the Covox mode (see Sound Cards, above), which is -b0. For Sound Blaster mode, use -b1. -m: Scaling mode. Set to -m1 for maximum amplitude mode. In this mode, all amplitude data is scaled on the plot so that all amplitudes are scaled to the amplitude of the highest peak in the plot. Set to -m0 for log amplitude scaling; log amplitude scaling is in dB, so this may be more suitable for some signals. -m0 is the default. -l: Line mode. Set to -l1 for line plot mode. In this mode, lines are drawn between points corresponding to amplitudes of successive bands. Set to -l0 for bar graph mode. In this mode, each frequency band is plotted distinctly, from the bottom of the plot to each amplitude point. -l0 is the default. -c: Cosine envelope. Type -c to turn on the cosine envelope function. This adds a filter that prescales the data to remove discontinuities at either end of the waveform before entering the FFT routine. This may produce a more stable display for waveforms that are not rapidly changing. -s: Squelch mode. To remove low-level noise from the input, to clean up the plot, use -s. This removes any samples above and below the zero level. For example, -s10 will remove all PCM samples between -10 and +10. Use this option carefully, since it can create square-waves, which have a variety of frequency components that will polute the spectrum. I do not recommend values of greater than, say 10. -e and -v: Force EGA or VGA mode, respectively. The default is to use the maximum resolution of the monitor, based on the mode the monitor is set to when MicFFT is started. -e has lower resolution, but may be faster on some VGA monitors. It also produces a somewhat larger plot. -v was added for consistency. Note that all options can be entered using either the - or / switch. Case is not important, but you must not include white spaces for any particular flag, since MicFFT will ignore any options that do not conform to this syntax. Order is also not important, since the options are collected and verified before any setup occurs. I recommend that you create a batch file that has your required configuration (for example, port and plotting mode specs) along with a couple of %n's to allow additional parameters to be entered. For example: @echo off REM RUNMF.BAT -- Batch for running MicFFT with set config. MicFFT -p24Fh -m1 -l1 %1 %2 %3 %4 Performance: As stated above, MicFFT frequency accuracy should not be affected by different machine speeds, since the sampling is done in a loop separate from the other routines, and uses the PC's internal 8253 timer chip for accuracy in the fractional microsecond range. However, the Sound Blaster mode may not be as accurate, because a number of additional steps are required for sampling that will certainly increase the processing time. Since I don't have a Sound Blaster card, it is not possible for me to test this out. Chris Pye, who wrote the Sound Blaster routines, has observed frequency problems, but only when the sampling rate exceeded 13 kHz. Try this out for yourself. If you use a tuning fork (or some other stable frequency generator), you should get approximately similar frequency peaks at different sampling frequencies. Keep in mind that any error introduced by this extra processing will affect high sampling rates. Thus, compare low rates with very high rates. If the frequency display is stable, everything should be pretty accurate. I have noticed that it is not possible to sample at a rate higher than 34090 Hz (not even 34091!) on the Covox card. When I try, I get no output (or output only in the first channel). I don't know why this occurs, but it is probably related to the way in which this specific card samples data, as well as my machine's clock rate (33 MHz). I assumed that I would see a smearing of frequency at these higher rates (i.e. shifting to reflect a lower actual rate than set by the program), but rather this is a brick wall beyond which sampling doesn't work. In a way, I much prefer this, since it helps to know that the program is accurate upto this maximum rate. Again, it is important to test this out on each system, if you are really interested in accurate, high-frequency sampling. In this respect, I may move to DMA-controlled PCM sampling support for the Sound Blaster Pro and Pro Audio Spectrum cards in future releases. This would allow the card itself to do the work of ensuring accurate sampling. The refresh rate (i.e. the amount of time between sampling periods) will vary, depending on the machine used. MicFFT is set up to sample 256 data points, transform and plot out the data, then repeat this. On slow machines, the refresh rate will be low; on fast machines, particularly those equipped with floating-point coprocessors, it will be impressively fast. Nevertheless, it is important to stress that the time spent processing the data is time spent not sampling. Thus, events occuring between sampling periods will be ignored. This may be problematic with time-varying signals, particularly those with substantial transient components. For this reason, it is necessary to carefully analyze the plot for such data. Sometimes, the plot will miss these transients. If this is a concern, I suggest slowing the sampling rate to the lowest allowable frequency (based on the bandwidth of the signal), as this will increase the chance of capturing this varying signal in the plot. You can freeze a waveform, but this is difficult with rapidly varying signals. A more suitable approach would be to sample the waveform and select the parts of a time-domain plot to display. Future versions of MicFFT will include this feature. Also, it is important to be cognisant of the Nyquist limit for any particular waveform, as signals with components exceding the limit will be "aliased" and not represented properly by the spectral plot. As I described above, frequencies above the Nyquist limit will produce errors (aliasing) unless these are removed from the signal before they are sampled. This is interesting in one respect: set the sampling frequency to about 4000 Hz and start a low whistle. As you increase the frequency, you will notice that the peak wraps around as it moves to the right side of the plot. If it goes far enough, it will also wrap around the left side of the plot as well. This a very graphic demonstration of aliasing. Beyond the academics, aliasing can be a serious problem to accurate spectral analysis. MicFFT does not yet have any low-pass filtering built in (although future versions may include this), so you will have to consider aliasing when chosing a particular signal and sampling frequency. If you are capable, it is possible to add a low-pass filter to the input line of your signal generator (or mic) to eliminate these higher frequencies. Your sound card may even provide for this type of bandwidth limiting. MicFFT is not designed to compete with hardware spectrum analyzers (not yet, at least). But, since these hardware analyzers are many thousands of dollars, the cost of this approach is more suitable for many applications, particularly experimentation into sound, etc. Although you may come up with interesting ideas, I don't yet recommend its use in building the next-generation Hubble Telescope, etc. However, it might work really well in analysis of Cold Fusion experiments. If you have any results in this arena, please inform me so I can buy the stock (SEC, just kidding already!). Acknowledgements: I'd like to take this opportunity to thank many of you who downloaded MicFFT v1.0 and sent comments to me about the program. Since I've not asked for a fee for the program, at least it gives me a little ego boost, and makes the programming a bit more fun. Chris Pye has been instrumental in making MicFFT compatible with Sound Blaster cards. He also provided code for the freeze- window routine and the cosine-envelope option. He knows a lot more about Fourier transforms than I (I'm a molecular biology grad student, and just a engineering/physics hacker), and I'll be working with him a lot in the future for developing better versions of the program. Additionally, the FFT routines used in this program are based on those implemented in an archive called FFT.ARC found on Compuserve by the author Steve Sampson, as well as those found in a book called Numerical Recipes in C. The 8253 timer routines (which have extraordinary accuracy) are based on a Compuserve archive called TIMERH.ARC, uploaded by the author Micahel Walraven. I am indebted to the work of these authors. Conditions of Use: MicFFT v1.1 is currently freeware. However, if you use the program, I ask that you contact me (see Contacting The Author) to let me know what you are using it for, its fitness, and other comments, problems, etc. When and if I decide to charge for my work, I'll won't require this. When I download programs I find interesting, I often notify the author out of courtesy. Usually, I get lots of ideas as well. You may find that such discourse can be fun and interesting. On the other hand, you may find that I don't know anything about this stuff. You'll just have to try me. The code for MicFFT is not available, unless you make specific arrangements with me first. The main reason for this is that I want to maintain control of the development of the program. If you have good ideas, and are proficient in coding, I'll make exceptions. Contacting The Author: You can contact me at the following E-mail addresses: Compuserve 70701,1614 Internet: walsh@biovx1.dnet.nasa.gov (Incidentally, I don't work for NASA, but our mail-server here at UCLA is named this way for some strange reason). I can also be contacted by phone at my Los Angeles residence at (310) 390-0598 Please note that I'd prefer to get mail via Internet, since my Compuserve bills have been skyrocketing (and I'm just a poor, lowly grad student). You can do this on Compuserve by sending the mail to an Internet address (see the help screen for the specifics here. I don't recall offhand how to do this). I check my mail on the Internet on a daily basis; I check Compuserve much less frequently. For a super low-tech approach, you can send a post via hardcopy to: Craig Walsh 12420 Woodgreen Ave #203 Los Angeles, CA 90066 Have fun, and good luck with MicFFT v1.1. Let me know what you think.