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10 Pages

### good projectDigital Signal Processing

Course: CSIE 123, Spring 2012
School: Hutchinson CC
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Word Count: 1064

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to ECE645 Introduction Digital Signal Processing Project Report Submitted By Damanjit Singh Nirupama Zambre Objective: To change the sampling frequency of a given digital signal Steps: 1. We use a music file sampled at 44.1 KHz in .wav format. Matlab has functions like wavread to read the .wav file and convert it to data file for further processing and wavwrite to write the processed output to .wav file. 2. Up...

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to ECE645 Introduction Digital Signal Processing Project Report Submitted By Damanjit Singh Nirupama Zambre Objective: To change the sampling frequency of a given digital signal Steps: 1. We use a music file sampled at 44.1 KHz in .wav format. Matlab has functions like wavread to read the .wav file and convert it to data file for further processing and wavwrite to write the processed output to .wav file. 2. Up sampling- The operation of up sampling by a factor L N describes insertion of L-1 zeros between every sample of the input signal. i.e. padding data with intermediate zero valued samples. 3. Low pass filtering- We are using IIR filters for low pass filtering. We choose an Elliptic filter (LP IIR). Forward and backward processing is done to eliminate the effects of non-linear phase characteristic of the filter, at each stage of low pass filtering. 4. Down Sampling- The operation of down- sampling by a factor of D N describes the process of keeping every D th sample and discarding the rest i.e. retaining only one out of the N samples of the filtered output. For our project, we want to convert sampling frequency of 44.1 KHz to 48 KHz i.e. we need to re-sample our signal by the following ratio: 48 480 10 8 6 = = 44.1 441 9 7 7 Here, the first step would be up- sampling by L=10, then low pass filtering followed by down- sampling by D=9. Then repeat this for L=8 and D=7, and then with L=6 and D=7. Description and Details: We read 100*1024 (100k) samples of music file Chellame S1.wav uploaded on the website using wavread and store data in orgData, the sampling frequency in Fs and the number of bits in bits. Full size of the given file could not be taken because its size was too large to fit into MATLABs memory. The above read samples are written to input.wav file using wavwrite for comparison purposes. We now plot FFT of the sample music file (input.wav or orgData) to observe the spectrum of the given signal (data): 1 FFT of original/input data 350 300 Magnitude --> 250 200 150 100 50 0 0 2 4 6 Frequency --> 8 10 12 4 x 10 In the FFT of the sample music file, we observe two colors blue and green. This is because of the presence of two channels. The sample music file gets stored in orgData in form of two columns, one for each channel. The sampling frequency is Fs = 44.1 KHz per channel. In up- sampling the spectrum gets compressed by a factor of L. We plot the FFT after every up- sampling to see if the processing is proceeding as desired. Up- sampling for L=10, we should be able to see 10 peaks. 2 FFT after upsampling of data 350 300 Magnitude --> 250 200 150 100 50 0 0 2 4 6 Frequency --> 8 10 12 5 x 10 Design of Elliptic filter (for low pass filtering) - We use fifth order Elliptic filter (N=5), passband ripple Ap=1.25 dB, the stop band attenuation for As=40.27, =1 and the filter ratio (ratio of stop band and cut off frequency) s / c =1.2062. We find the coefficients for normalized 5 th order elliptic filter using the table given in the class notes. That is, we take the following values 0 = 0.35693; 1 = 0.20145; 2 = 0.04529; 1 = 0.73787; 2 = 0.9946; 3 = 1.2402; 4 = 1.7368; And substitute them in the following given equation of fifth order elliptic filter: T ( s) = K ( s 2 + 32 )( s 2 + 42 ) ( s + 0 )( s + 1 j1 )( s + 2 j 2 ) We find the value of K by using the fact that the dc response of an odd order Elliptic filter is unity and thus obtain the analog normalized low pass filter. We then convert it to a filter digital using the following transformation from analog normalized low pass filter. 3 That is, we perform pre-warping and bilinear transformation in a single step. Then forward and backward processing is performed to eliminate the effects of non-linear phase characteristic of the filter, at each stage of low pass filtering. That is, a symmetric low pass filter is used with the same magnitude characteristic but phase characteristic negative to that of the original in series with the original filter. Thus, converting it to a zero phase filter. Note that as one of these filters (forward or backward processing filters) will be non-causal, this processing is possible only on the stored data and not the data which is coming in real time. After the low pass filtering, we plot the FFT to verify the design of our elliptical low pass filter: FFT after low pass filtering of data 350 300 Magnitude --> 250 200 150 100 50 0 0 2 4 6 Frequency --> 8 10 12 5 x 10 4 The last step is down- sampling. Here the spectrum expands by a factor of D. In order to avoid aliasing, all the frequencies should be within 1/D of cut-off frequency Fc, otherwise the spectrums will overlap. We plot the FFT after every down- sampling to see if the processing is proceeding as desired. FFT after down sampling D=9, FFT after down sampling of data 350 300 Magnitude --> 250 200 150 100 50 0 0 2 4 6 Frequency --> 8 10 12 4 x 10 We repeat the above process of up-sampling, low pass filtering and down sampling two more times as mentioned in the beginning (L=8 & D=7, L=6 & D=7). The FFTs obtained during these two repetitions are given below: Up- sampling for L=8, we should be able to see 8 peaks. 5 FFT after upsampling of data 350 300 Magnitude --> 250 200 150 100 50 0 0 1 2 3 4 5 6 Frequency --> 7 8 9 10 5 x 10 FFT after low pass filtering FFT after low pass filtering of data 350 300 Magnitude --> 250 200 150 100 50 0 0 1 2 3 4 5 6 Frequency --> 7 8 9 10 5 x 10 6 FFT after down sampling D=7, FFT after down sampling of data 350 300 Magnitude --> 250 200 150 100 50 0 0 2 4 6 8 Frequency --> 10 12 14 4 x 10 Up- sampling for L=6, we should be able to see 6 peaks. FFT after upsampling of data 350 300 Magnitude --> 250 200 150 100 50 0 0 1 2 3 4 5 Frequency --> 6 7 8 5 x 10 7 FFT after low pass filtering FFT after low pass filtering of data 350 300 Magnitude --> 250 200 150 100 50 0 0 1 2 3 4 5 Frequency --> 6 7 8 5 x 10 FFT after down sampling D=7, FFT after down sampling of data 350 300 Magnitude --> 250 200 150 100 50 0 0 2 4 6 Frequency --> 8 10 12 4 x 10 8 This is the FFT of the processed signal. We write the processed signal using wavwrite to an output file called output.wav. Observations and Conclusions: We can now compare the size of files input.wav and output.wav. We find that the size of the output file has increased by the re-sampling ratio of (48 kHz/44.1 kHz). This is a check to ensure that the sampling frequency has been converted from 44.1 KHz to 48 KHz. On changing the sampling frequency from 44.1 KHz to 48 KHz, we listen to the Original data sample (at 44.1 KHz) and the processed data sample (at 48 KHz), we find that both of the music samples play the same. Hence, music on CDs (digitized at 44.1 KHz) and same music on DVD (digitized at 48 KHz) use different sampling frequencies to represent the signal. 9
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