Revision as of 19:37, 6 September 2011

Sampling of an A 440

Explain how one can use MATLAB to play an A 440. Discuss your choice of sampling rate. (Feel free to post a sound file of your output.)

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Answer 1

The signal we want is $ x(t) = cos(440 * 2\pi) $.

We can first create a vector of sample times. In this case, we'll let the sample frequency be 1320 Hz over a sample interval of [0,1]

t = 0:(1/1320):1;

Next, we can generate the sound samples vector from the sample times vector.

y = cos(440*2*pi*t);

Finally, we play the signal by using the "sound" command, which needs the user to specify the sound vector and the sample rate of that vector. Our sample was 1320.

sound(y, 1320);

The sample frequency was chosen so that it was more than twice the note frequency, so that the signal could be completely recovered from this sample.

Instructor's comments: Did you actually try it in MATLAB? Did it work? -pm

Answer 2

I chose the sample rate to be 1/1000.

n = 1:10000;

x = cos(2*pi*400*n/1000);

x = x';

sound(x)

Answer 3

% The following script plays a pure note A-440.

% It provides an adjustable sampling rate.

sampling_rate = 1500;

% Sampling rate should be larger than Nyquist Rate, i.e. 880Hz in this case.

t = 1:(1/sampling_rate):3;

x = cos(2*pi*440*t);

sound(x,sampling_rate);

%Code had been verified on MATLAB R2010b

Answer 4

rate=1/1000 t=0:rate:5; x=cos(440*2*pi*t); sound(x,1/rate)

the code works

Answer 5

samplerate=1/44100;

t1=0:samplerate:5;

x=cos(440*2*pi*t1);

sound(x,1/samplerate);

I just picked the sampling rate

because it is most commonly used rate for digital audio such as MP3.

This sampling rate is sufficient for anything in the hearing range.

Answer 6

To play a pure tone of 440 Hz, a sampling rate of only at least 2*440 = 880 Hz is needed.

However for humans to pick up the entire contribution of the signal harmonics, a sampling rate of 44.1 kHz should be used. This types out in matlab to

freq = 44100;

t=0:(1/freq):3; %for a tone of 3 second duration

x = cos(2*pi*440*t);

sound(x,freq)

Answer 7

- The sampling rate should be atlease 880Hz (Nyquist Rate)

- let rate=5000

- Constructing sine wave

- t = 0:(1/rate):1;

- A=cos(440*2*pi*t);

- Playing the sound

- sound(A,rate)

Back to ECE438 Fall 2011 Prof. Boutin