Case Study - 3 Signal Processing Lisa Simpson: Would you guys turn that down! Homer Simpson: Sweetie, if we didn't turn it down for the cops, what chance do you have? "The Simpsons" Little Big Mom (2000) Acceptance tests for a real-time signal processing system are presented. It s Too Loud I have produced software with Richard Cann of Grozier Technical Systems for a number of years. Grozier produces sound level measurement systems. These systems are used by numerous concert sites, particularly outdoor ones, to monitor sound levels for regulatory reasons and to act as good neighbors. The systems are composed of embedded systems which run multiple programs. Richard produces some of the programs, particularly the display and control version. I produce the real-time signal analysis portion. (** Ref http://en.wikipedia.org/wiki/sound_level_meter **) Hardware The programs use the integrated sound chip (AC 97) that is standard on many embedded Windows computers). Those chips convert sounds of a single channel up to 96000 samples per second and two channels up to 48000 samples per second. Conversion at 48000 samples per second are good for sounds up to 24 KHz. This is due to Nyquist sampling issues, which is well beyond the scope of this book. (see ***) (** Ref http://en.wikipedia.org/wiki/ac%2797 **) (** Footnote The original signal capture programs used a stand-alone analog to digital converter (A/D) A separate A/D has certain advantages as it can convert frequencies well past normal hearing levels up to 200 KHz or more. ***) (** Ref http://en.wikipedia.org/wiki/nyquist%e2%80%93shannon_sampling_theorem ** ) Sound Levels The signal analysis programs perform calculations every second. The main measure is the equivalent continuous sound level (Leq) every second. Leq is a common way of referring to Lat. For those mathematically inclined, Lat is 20 times the base 10 logarithm of the ratio of the root-mean-square A-weighted sound pressure during a time interval to the reference sound pressure. The reference sound pressure is the threshold of human hearing, about the sound of a mosquito flying 3 meters away. The perceived loudness of a sound correlates roughly logarithmically to its sound pressure. 186
The process as shown in Figure X.1 starts by converting the analog sound signal to a series of one second s worth of samples. Analog Digital Conversion (Hardware Audio Apply Window Windowed Apply A-Weight A- Weighted Compute RMS and log Leq Figure X.1 Sound Level Process The cutoff at the beginning and the end of each second create spurious frequencies, so the samples are Hann windowed. Then the sample is A-weighted (as shown in Figure X.2). Finally the Leq is computed. (** REF See http://en.wikipedia.org/wiki/window_function **) (** Ref See : http://en.wikipedia.org/wiki/a-weighting **) Gain in db versus Frequency Figure X.2 A-Weight 187
The sound is input through a microphone. The gain (how much the signal is amplified) varies based on both the microphone and the volume setting on the input. To correctly compute the Leq, the gain must be adjusted so that a standard sound source (a calibration source) produces a specific Leq result. The calibration source is a highly controlled sound generator. The output is feed to the microphone used for measuring the sound level. This calibration is part of the setup. It is difficult to replicate the entire system (microphone, calibration source, and so forth) for testing. However the sounds can be captured by regular recording methods and then replayed as input for the tests. Suppose the sounds produced by the calibration source are captured in a calibration file. And that sounds of known Leq are also captured in separate files. Then the test of the overall system can be: ***Start Background Given that the volume is adjusted so that calibration file (containing a 1 KHz signal) yields the standard Leq: Calibration File Leq (db) calibration.wav 94 Then the test files should be produce values of the expected Leq. Leq Tests Input File Leq (db)? test1.wav 88 test2.wav 95 ***End Background In order to ensure that these Leq s are correct, the same test can be repeated with calibrated specialized hardware. The process of comparing two separate ways of calculating an output and comparing them is similar to comparison of the outputs the multiple flight control algorithms that the space shuttle employs. Each algorithm computes a path. If all results agree, everything is great. If one differs, the shuttle uses the results that majority agree with. If every result is different, well, that s what makes for an interesting flight who do you believe? Developer Tests Richard is particularly interested in the final results is the Leq computed correctly for a particular file? However as a developer, it helps if I can apply tests to intermediate results. These intermediate tests would usually be termed unit tests, since they apply to lower level modules. However, since Richard is highly experienced in signal processing, he creates input and output files that can be used to ensure that the intermediate processing works correctly. For example: AWeight Test Files Input file Aweight1.data Aweight2.data Output file? Aweight1-out.data Aweight2-out.data The input and output files contain digital samples for one second. Equivalent files are available for each of the other steps in the process. 188
I Can t Hear It For other sound measurement applications, you need to measure the sound pressure in a set of frequency bands. Each frequency band has a low and a high frequency cutoff. Measuring in bands requires creating a band-pass filter that eliminates frequencies that are lower than the low frequency and higher than the high. The process is shown in Figure X.3. A common standard for frequency bands is: Frequency Bands Center Frequency Low Frequency High Frequency 31.5 22 44 63 44 88 125 88 177 250 177 354 500 354 707 1000 707 1414 2000 1414 2828 4000 2828 5656 8000 5656 11312 (*** See http://www.osha.gov/dts/osta/otm/noise/health_effects/physics.html ) Analog Digital Conversion (Hardware Audio Apply Window Windowed Apply Filter For each Band for each Band Compute RMS and log for each band Db for each band Figure X.2 Frequency Band Filtering The acceptance tests for this follow along the same lines as the previous tests. However they now involve different values for each frequency. There are a number of tests. The first set of test cases involves the input of tones at particular frequencies. The values of other frequencies should be relatively smaller. The examples given in this table are for a first-order filter. Frequency Band Levels Single Frequency Files Input File 31.5 Hz? 63 Hz? 125 Hz? 250 Hz? 500 Hz?.. and so 189
Freq31.5.wav 1.0.25.062.016.004 Freq63.wav.25 1.0.25.062.016 Freq125.wav.062.25 1.0.25.062 Freq250.wav.016.062.25 1.0.25 Freq500.wav.004.016.062.25 1.0 and so forth forth If the individual tones test properly, then another set of tests is run. These test use actual or simulated samples of sound. The values for each band are determined either by an alternate sound processing system, such as hardware, or by the values used to create the simulated samples. Frequency Band Levels Mixed Sounds Input File 31.5 Hz? 63 Hz? 125 Hz? 250 Hz? 500 Hz?.. and so forth Sample1.wav.2.31.41.31.92 Sample2.wav.5 1.0.9.5.2 and so forth Summary Acceptance tests do not have to involve just simple values. They can be entire sets of values (usually represented in files) A subject matter expert can often create lower level tests that can be used as unit tests Tests for real-time systems may run for a while 190