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Project 1 Summary Form-1

# Project 1 Summary Form-1 - Name_Li Yan UFID_51413909...

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1 Project 1 Summary Form Part 1.a: Implement, observe, quantify, and qualify the composite sinusoidal signal. What are the 5 utilized frequencies: f 0 689.00Hz ; f 1 1160.53Hz ; f 2 773.68Hz ; f 3 5512.50Hz ; f 4 8820Hz 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 x(t) waveform of the constructed signal 0 0.5 1 1.5 2 2.5 3 3.5 0 2 4 6 8 10 12 14 x 10 4 w X(w) spectrum of the constructed signal ----------- Display magnitude spectrum – FFFT(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. Part 1.c: Under-sampling experiment Name:__Li Yan ________________ UFID:______51413909 ______________

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