Project 1 Fall 2011

Project 1 Fall 2011 - Project 1: Sampling Common Sense...

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Project 1: Sampling Common Sense Caveat: If you need to modify a problem in order to obtain a meaningful outcome, do so but do so using common sense. The object of the Project 1 is to provide an inquiry-based experience in exploring sampling and sampling limitations. The study makes direct use of Shannon’s Sampling Theorem but requires that you properly interpret this signal processing tool. Part 1.a: Implement, observe, quantify, and qualify the composite sinusoidal signal. Construct the audio signal x[k] defined below, sampled at f s = 44.100Sa/s, with a signal duration around 5 seconds (choose a signal length N to be a radix-2 number). The signal x[k] consists of 5 distinct sinusoidal components satisfying: ( 29 ( 29 ( 29 ( 29 { } Hz range the in s frequencie of Range random uniformly j j j f f f k f k x Hz f f f k f k x k x i k x k x s i s i i s s i i 14700 , 441 ) ( ] 100 , 3 [ ; / ; ) / 2 cos ] [ 689 64 / ; ) / 2 cos ] [ amplitude decreasing ; ] [ 1 / 1 ] [ ] [ 0 0 0 4 1 0 = = = = = + + = = π Analyze the signal spectrum and listen to x[k] (MATLAB SOUND). MATLAB Code Snippet » nn=0:1:1023; » fs=44100; f0=fs/64; % 689 Hz » x=cos(2*pi*f0*nn/fs); % cosine » [X,w]=freqz(x); % generate spectrum - could also have used X=abs(fft(x))
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Project 1 Fall 2011 - Project 1: Sampling Common Sense...

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