Project+1+Summary+Form-2

Project+1+Summary+Form-2 - Name: Li Yan UFID: 51413909_...

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Project 1 Summary Form (v1.1) Part 1.a: Implement, observe, quantify, and qualify the composite sinusoidal signal. What are the 5 utilized frequencies: f 0 689.00Hz ; f 1 668.18Hz ; f 2 11025.00Hz ; f 3 518.82Hz ; f 4 474.19Hz Display the magnitude frequency response using an FFT (identify all relevant frequencies in Hz. 0 1 2 3 4 5 6 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 time (s) x(t) waveform of the constructed signal 0 0.5 1 1.5 2 2.5 x 10 4 0 2 4 6 8 10 12 14 x 10 4 w (Hz) X(w) spectrum of the constructed signal ----------- Display magnitude spectrum – FFT(x[k]) ------------------- Part 1.b: Reduce the sample rate. Is the time duration of the re-sampled signal the same, longer, or shorted than the parent signal? It is the same with the parental signal. Do x[k] and y[k] sound the same, generally similar, often dissimilar, or totally different? In most cases, there is conspicuous difference between x[k] and y[k]. How is you answer interpreted in the context of Shannon’s Sampling Theorem? At the sampling rate of 44100Hz, which is higher than two times of human’s hearing limit, 20000Hz, there is no obvious difference between x[t] and x[k]. However, after dividing the sampling rate by 4, the sampling rate has been reduced to 11025Hz, which is lower than two times of the bandwidth of x[t]. Therefore, reconstructible sampling is not guaranteed and aliasing may occur in most cases. 1 Name: Li Yan UFID: 51413909 ___________
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Part 1.c: Under-sampling experiment Display the magnitude frequency response of x[k] calibrated over f [0,f s /2=22050Hz] and that of y[k] calibrated over f [0,f s /8=5512.5Hz] 0 0.5 1 1.5 2 2.5 x 10 4 0 200 400 600 800 1000 1200 original signal w (Hz) X(w) 0 1000 2000 3000 4000 5000 6000 0 100 200 300 400 500 downsampled signal w (Hz) Y(w) 0 0.5 1 1.5 2 2.5 x 10 4 0 200 400 600 800 1000 1200 low-filtered signal w (Hz) Z(w) 0 1000 2000 3000 4000 5000 6000 150 200 250 300 low-filtered downsampled signal w (Hz) W(w) Note: It can be noticed that y[k] has suffered from aliasing, but w[k], which is processed with a low-pass filter, suffers no aliasing
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Project+1+Summary+Form-2 - Name: Li Yan UFID: 51413909_...

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