93 Set. 5.2. Telephone Touch-Tone 6). Create a MATLAB function that takes as input a sequence x of arbitrary length and calculates N equally spaced frequency samples of its DTFT. The first line of your function should be function X-dtft(x,) Be sure that your function works properly for both the case when N > M, and N> who Your variables are: hardxi hardx2 x2 The vectors xi and x2 contain sampled versions of the sequence of touch-tones representing two different phone numbers. As in Part (c), the signals consist of 7 digits of 1000 samples each, separated by 100 samples of silence. The vectors hardx1 and hardx2 are less precisely dialed versions of the same numbers that are used in Part (i). (d). Using fft, compute 2048 evenly spaced samples of the DTFT for each digit of xi. In order to apply fft to each digit separately, you will need to segment the signal into seven digits using the information you have about the relative lengths of the x1 95 Sec. 5.2. Telephone Touch Tone digits and spaces, or by plotting the signal and identifying when each digit starts and stops. Apply fftshift to the output of fft, which will rearrange the samples of the DTFT so they correspond to ascending frequencies in the range - Sw* > testout - ttdecode(phone) >> testout testout - 55 5 7319 The first line of the M-tile you write to implement the function should read function digits - ttdecode(x) Your function should use fft to compute 2015 samples of the DTFT of each digit in , and then check the energy at the samples you specified in Part (f) corresponding to ther for the touch-tones. Pick which of the row frequencies and column frequencies has the most energy, then use those frequencies to determine what the digit is. Test 96 CHAPTER 5. THE DISCRETE TIME FOURIER TRANSFORM your function by using xi and x2 as inputs and verify that it returns the same phone numbers you obtained in Parts (d) and (e). Also, test your function on the signal you created in Part (c) to represent your own phone number. (i). Most people do not dial their telephone with the ruthless precision wwumed in this exercise, with each digit exactly the same length and the space between digits always the same length. Modify your function to work with touch-tone signals where the digits and silences can have varying lengths. To simplify things slightly, me that all the tone and silences are at least 100 samples long. Verify the new version of your function works with the signals hardxi and hardx2. These signals contain the same tones 1 and 2, but they are not regularly spaced. 93 Set. 5.2. Telephone Touch-Tone 6). Create a MATLAB function that takes as input a sequence x of arbitrary length and calculates N equally spaced frequency samples of its DTFT. The first line of your function should be function X-dtft(x,) Be sure that your function works properly for both the case when N > M, and N> who Your variables are: hardxi hardx2 x2 The vectors xi and x2 contain sampled versions of the sequence of touch-tones representing two different phone numbers. As in Part (c), the signals consist of 7 digits of 1000 samples each, separated by 100 samples of silence. The vectors hardx1 and hardx2 are less precisely dialed versions of the same numbers that are used in Part (i). (d). Using fft, compute 2048 evenly spaced samples of the DTFT for each digit of xi. In order to apply fft to each digit separately, you will need to segment the signal into seven digits using the information you have about the relative lengths of the x1 95 Sec. 5.2. Telephone Touch Tone digits and spaces, or by plotting the signal and identifying when each digit starts and stops. Apply fftshift to the output of fft, which will rearrange the samples of the DTFT so they correspond to ascending frequencies in the range - Sw* > testout - ttdecode(phone) >> testout testout - 55 5 7319 The first line of the M-tile you write to implement the function should read function digits - ttdecode(x) Your function should use fft to compute 2015 samples of the DTFT of each digit in , and then check the energy at the samples you specified in Part (f) corresponding to ther for the touch-tones. Pick which of the row frequencies and column frequencies has the most energy, then use those frequencies to determine what the digit is. Test 96 CHAPTER 5. THE DISCRETE TIME FOURIER TRANSFORM your function by using xi and x2 as inputs and verify that it returns the same phone numbers you obtained in Parts (d) and (e). Also, test your function on the signal you created in Part (c) to represent your own phone number. (i). Most people do not dial their telephone with the ruthless precision wwumed in this exercise, with each digit exactly the same length and the space between digits always the same length. Modify your function to work with touch-tone signals where the digits and silences can have varying lengths. To simplify things slightly, me that all the tone and silences are at least 100 samples long. Verify the new version of your function works with the signals hardxi and hardx2. These signals contain the same tones 1 and 2, but they are not regularly spaced