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Filtered Audio Demo
Max Kamenetsky
In this demo you'll listen to a 10 second segment of music, alternating with various ltered versions of it. You should try to relate what you hear to the frequency resp onse, impulse and step resp onses, and snapshots of the input and output signals.
First order lowpass lter
The rst lter is a rst order lowpass with cuto frequency 1kHz, with transfer function
H (s) =
!c s + !c
1 + s=!c
where !c = 2 1000. Note that it passes frequencies under around 500Hz or so, but attenuates high frequencies. Since it attenuates high frequencies the ltered segment will sound a bit mued. (A higher order lowpass lter, with a sharp er cuto characteristic, would sound much more mued.) The impulse resp onse shows that this lter smo oths out the input, giving a sort of averaging over a few milliseconds. You can see that the ltered signal is a smo othed version of the original signal.
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1−pole lowpass (Fc = 1kHz) Bode plot
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1−pole lowpass (Fc = 1kHz) impulse response
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1−pole lowpass (Fc = 1kHz) step response
0 0.5 1 1.5 2 2.5 3 3.5 4 4. x 10−
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Original signal
0 0.5 1 1.5 2 2.5 3 3.5 4 4. x 10−
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1−pole lowpass (Fc = 1kHz) filtered signal
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1−pole highpass (Fc = 1kHz) impulse response
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1−pole highpass (Fc = 1kHz) step response
δ(t)
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Original signal
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1−pole highpass (Fc = 1kHz) filtered signal
Low Q bandpass lter
This is a second order bandpass lter, with center frequency 1 kHz and Q = 4. Transfer function: H (s) = K
s (Q=!c )s^2 + s + Q!c
where Q = 4, !c = 2 1000, and K = 6 : 7 16 : 5 dB is a scale factor to increase the volume level. Here frequencies b etween 500Hz and 2kHz or so are passed, and b oth low and high frequencies are attenuated. The acoustic e ect is something like listening through a tub e (which has resonances | you'll learn ab out that in EE141!). You can also hear when a note (or a harmonic) gets near 1kHz. The impulse resp onse is oscillatory, and you can see the e ect in the plot of the ltered signal. Here b oth the fast wiggles and the slow undulatations are attentuated.
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First order bandpass (center = 1kHz, Q = 4) Bode plot
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High Q bandpass lter
Second order bandpass lter with center frequency 1kHz and Q = 40. Transfer function:
H (s) = K
s (Q=!c )s^2 + s + Q!c
where Q = 40, !c = 2 1000, and K = 28 29 dB is a scale factor to increase the volume level. Here the frequencies near 1kH are strongly emphasized, which is quite annoying. The impulse resp onse is quite oscillatory, which you can also see in the plots of the ltered signal.
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First order bandpass (center = 1kHz, Q = 40) Bode plot
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First order bandpass (center = 1kHz, Q = 40) impulse response
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First order bandpass (center = 1kHz, Q = 40) step response
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Original signal
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First order bandpass (center = 1kHz, Q = 40) filtered signal
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First order allpass impulse response
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First order allpass step response
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First order allpass filtered signal
Moving average lter
This lter is a 10ms moving average lter. Impulse resp onse:
h(t) =
K (1= 0 :1); 0 t < 0 : 01 0 ; t 0 : 01
The DC gain is K , which we take to b e K = 3 : 5 10 :9dB to increase the volume level. In this case the ltered signal output is exactly (K times the) average of the input signal over the last 10ms. Here the ltered signal sounds very mued; the high frequencies are strongly attenuated.
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10 ms moving average Bode plot
Filter with echos
Impulse resp onse:
h(t) = Æ (t) + 0 : 75 Æ (t 0 :125) 0 : 1065 Æ (t 0 :1536) 0 : 4098 Æ (t 0 :1605) + 0 : 0308 Æ (t 0 :1788) + 0 : 0705 Æ (t 0 :1934) 0 : 2804 Æ (t 0 :2201) + 0 : 2906 Æ (t 0 :243) + 0 : 2898 Æ (t 0 :2567)
This represents 8 p erfect echos. The rst one arrives 125ms after the rst impulse, and the others come over the next 125ms or so.
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Hall echos Bode plot
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Hall echos impulse response
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Hall echos step response
−0.2 0.227 0.2275 0.228 0.2285 0.229 0.2295 0.23 0.2305 0.231 0.
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−0.2 0.227 0.2275 0.228 0.2285 0.229 0.2295 0.23 0.2305 0.231 0.
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Hall echos filtered signal
