ECE 3084 OCTOBER 17, 2017

Transcription

1 Objective ECE 3084 LAB NO. 1: MEASURING FREQUENCY RESPONSE OCTOBER 17, 2017 The objective of this lab is to measure the magnitude response of a set of headphones or earbuds. We will explore three alternative strategies: One based on feeding a noise-like signal to the headphones, another based on feeding a linear chirp signal, and a third based on feeding an impulse train. Tools You Will Need This lab requires only four tools: (i) a pair of headphones or earbuds; (ii) a microphone (which could be the built-in microphone of your laptop); (iii) sound recording software; (iv) a laptop with MATLAB. Before coming to lab, be sure you are able to (1) record a sound using the microphone, and (2) save it to a WAV file. A word of warning: By default, the sound recorder on a Windows 7 machine will save to WMA format, whereas MATLAB prefers to load audio in WAV format. You could later convert from WMA to WAV after the fact, but you may find it easier to create a shortcut for sound recorder, and to specify the target of the shortcut as: %SystemRoot%\system32\SoundRecorder.exe /file C:\Users\You\Desktop\LAB\recording.wav The key point here is that the filename extension of.wav ensures the proper format. Approach Our aim in this lab is to measure the magnitude response of the cascade of a set of headphones and a microphone. As shown in Fig.1, we will use the MATLAB soundsc command to play a sound s( t ) on the headphones, and use sound recorder software and the MATLAB wavread command to load a sampled version of the recorded waveform r( t ) into MATLAB: The overall cascade of the headphones and the microphone with input s( t ) and output r( t ), is accurately modeled as an LTI system with impulse response h( t ), so that the overall frequency response H(j ) decomposes into the product of the frequency response of the headphones and microphone, namely H(j ) = H 1 (j )H 2 (j ). This lab will compare three different strategies for experimentally measuring the magnitude response: transmit noise; pass the recording through a filter matched to the noise to estimate h( t ); take the Fourier transform of h( t ). transmit a chirp; use the envelope of the recording as an estimate of H(j ). transmit a pulse train; average the responses to the pulses to estimate h( t ); take the Fourier transform of h( t ). These three strategies are compared in Fig.2.

2 s soundsc DAC s( t ) r( t ) sound r.wav recorder ADC wavread r LAPTOP LAPTOP PHONES MIC s( t ) r( t ) H 1 (j ) H 2 (j ) s( t ) r( t ) H(j ) Fig. 1. The experimental setup. The equivalent model is a cascade of two systems. (c) The overall system has frequency response H(j ) = H 1 (j )H 2 (j ). s 1 ( t ) = NOISE h( t ) r( t ) s 1 ( t) MF y( t ) EXTRACT SEGMENT h 1 ( t ) FOURIER TRANSFORM H 1 (j ) s 2 ( t ) = CHIRP h( t ) r( t ) ENVELOPE DETECTOR H 2 (j ) s 3 ( t ) = PULSE TRAIN h( t ) r( t ) AVERAGE SEGMENTS h 3 ( t ) FOURIER TRANSFORM H 3 (j ) Fig. 2. Three strategies for estimating the magnitude response: Transmit noise, and use a matched filter to estimate h( t ); Transmit a chirp, and use an envelope detector to estimate H(j ) ; (c) Transmit a train of impulses, and average the responses to estimate h( t ). The three different types of probing signals will be concatenated to produce one long signal, as shown in Fig.3. At the beginning there is a noise signal s 1 ( t ) of duration T 1, followed by a silence gap of duration T gap, followed by a chirp signal s 2 ( t ) of duration T 2, followed by a silence gap of duration T gap, followed by an impulse train s 3 ( t ) of duration T 3. T 1 T gap T 2 T gap T 3 NOISE CHIRP IMPULSES 0 t Fig. 3. A noise signal of duration T 1, followed by a chirp of duration T 2, followed by an impulse train of duration T 3, separated by a gap of silence of duration T gap.

3 Part 1: Preparation (Pre-Lab) (Envelope detection) The second strategy requires an envelope detector. Here we will show how to implement an envelope detector in MATLAB. The following MATLAB code generates a sampled version of s( t ) = cos(20 t)g( t ), where g( t ) = sin( t)/( t) is a sinc function: fs = 44.1e3; t = -3:1/fs:3; s = cos(20*pi*t).*sinc(t); e = abs(hilbert(s)); plot(t,s,t,e); The line e = abs(hilbert(s)) computes the envelope e( t ) of s( t ). Verify from the plot that the envelope matches your intuition about what an envelope is. Explain how the envelope e( t ) differs from the sinc function g( t ). (Equipment Test) Record your own voice. Load it into MATLAB using: [r,fs] = wavread( recording.wav ); Confirm your ability to record and play back by executing the following command, and verify that what you hear is what you recorded: soundsc(r,fs); What is the sampling rate f s (in Hz) used by your recording software?

4 Part 2: Recording Experiment Save the following MATLAB routine to run2.m (changing fs to match above, if necessary), and run it: T1 = 2; T2 = 2; T3 = 2; Tgap = 0.01; fmax = 10e3; period = 0.01; fs = 44.1e3; N = round(t3/period); L = period*fs; % duration of noise % duration of chirp % duration of impulses % duration of silence gap % maximum chirp frequency % pulse train period % sampling rate % number of impulses transmitted % integer spacing between impulses rng(0); s1 = randn(1,fs*t1); % noise t2 = 0:(1/fs):T2; s2 = cos(pi*fmax*(t2.^2)/t2); % chirp t3 = 0:(1/fs):T3; s3 = 0*t3; s3(1:(period*fs):end) = 1; % pulse train silence = zeros(1,fs*tgap); s = [s1, silence, s2, silence, s3]; input('start recording, then hit return: ','s'); soundsc([s;s],fs); input('after sound ends: Stop recording, then hit return: ','s'); r = mean(wavread('recording.wav'),2); plot(r); Explain what you see in the different time regions of the plot. Zoom into the middle part. Do you see a sinusoid? Zoom into the ending part. Do you see an impulse train? Evaluate the spectrogram using: spectrogram(r,512,[],[],fs,'yaxis'); Explain what you see in each of the three different time regions of the spectrogram.

5 Part 3: Estimating Magnitude Response Save the following MATLAB routine to run3.m, and run it: run2; % record sound and load into MATLAB % locate starting indices using a matched filter y = conv(r,fliplr(s1)); % MF [ignore,ix] = max(abs(y)); % ix = index of maximum MF output i2 = ix + Tgap*fs + 1; % i2 = index of first sample of chirp i3 = i2 + (T2 + Tgap)*fs + 1; % i3 = index of first sample of pulse train % estimate impulse response from noise h1 = y(ix (1:L))/(sum(s1.^2)/fs); % estimate magnitude response from chirp f2 = linspace(0,fmax,t2*fs); H2 = smooth(abs(hilbert(r(i2+(1:t2*fs)))),(t2/200)*fs); % estimate impulse response from pulse train R3 = reshape(r(i (1:N*L)),L,N); h3 = mean(r3')*fs; % convert impulse response to magnitude response N = 2^13; Nmax = round(n*fmax/fs); H1=fft(h1,N)/fs; H1 = abs(h1(1:nmax)); H3=fft(h3,N)/fs; H3 = abs(h3(1:nmax)); f1 = linspace(0,fmax,nmax); plot(f1,h1,f2,h2,f1,h3); legend('noise','chirp','impulses'); The variable y is the output of a matched filter. What is it matched to? Plot y and explain what you see. (c) From the code we see that H2 is the smoothed output of an envelope detector with input r. Show where the shape of H2 appears when you plot r using plot(r). (d) Compare the three measured magnitude responses. Are they a good match? (e) How small can you make T1 = T2 = T3 and still get reasonable results? (f) How do the measurements change as T1 = T2 = T3 grows very large?

6 Part 4: Nonlinearity The headphone-microphone system is accurately modeled as a linear system, but it becomes nonlinear when the sound is so loud at the microphone that the microphone saturates. See if you can make the system nonlinear by a combination of turning up the volume and placing the microphone close to the headphones. Which of the three strategies for estimating the magnitude response works the best, despite the nonlinearity? What signs of nonlinearity can be found in the spectrogram of the recorded waveform?

7 ECE 3084 LAB NO. 1: INSTRUCTOR VERIFICATION Part 1. Preparation (Pre-Lab) NAME: Verify that abs(hilbert( )) is an envelope detector. The sampling rate is f s = Hz. Part 2. Recording Experiment After plot(r); Explain what you see in the different time regions of the plot. Zoom into the middle part. Do you see a sinusoid? Zoom into the ending part. Do you see an impulse train? Evaluate the spectrogram using: spectrogram(r,512,[],[],fs,'yaxis'); Explain what you see in each of the three different time regions of the spectrogram. Part 3. Estimating Magnitude Response The variable y is the output of a matched filter. What is it matched to? Plot y and explain what you see. (c) From the code we see that H2 is the smoothed output of an envelope detector with input r. Show where the shape of H2 appears when you plot r using plot(r). (d) Compare the three measured magnitude responses. Are they a good match? (e) How small can you make T1 = T2 = T3 and still get reasonable results? (f) How do the measurements change as T1 = T2 = T3 grows very large? Part 4. Nonlinearity Which of the three strategies for estimating the magnitude response works the best, despite the nonlinearity? What signs of nonlinearity can be found in the spectrogram of the recorded waveform?