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DFT can also be obtained using matrix multiplication. Let X[r] show the transformed values and x[n] show the original signal. Using the analysis equation: Using matrix multiplication, this operation can be written as x[O X[1 1 e(2m/N) e-K4n/N) x12] [N-1]] e-j(2(N-1)T/N)e-j(4(N-1)m/N) Instead of huilt-in EFT function use matrix multinlication to solve 3th auestion [ 1 e-/(2(N-1)(N-1)T/N)]Le[N-1] DFT is an extension of DTFT in which frequency is discretized to a finite set of values 0-(M-1). In most of the approaches M is equal to signal length (N). Thus, for an x[k] signal with length N, analysis and synthesis equations can be written as: Analysis Equation: X[r]= 0x(kle-jam for 0sr Synthesis Equation : x[k-12%-1xlrlejam for 0 k H-1 2π kr N-1 In this part of the homework, you will use DFT for audio visualization. Steps are given b for a basic audio visualizer 1. Select the visualization renewal rate (e.g. 10 FPS). Since you know the sample rate in Hertz (44100 in the given file.), you can select data from the audio array which is matching with renewal time. For example, to visualize at 10 FPS, each visualizatiorn interval comes from 4410 values in sampled audio matrix. Pad the audio matrix with zeroes if necessary 2. For each visualization interval, a. Find DFT of that interval using FFT(Fast Fourier Transform) function which is a fast way to calculate DFT with divide-and-conquer method. Since it's in exponential form, it will give an array of complex numbers. Find the magnitude of each value.

Answer 1

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