5. In audio processing, one often wants to find tonal sounds in segments of the recordings....

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5. In audio processing, one often wants to find tonal sounds in segments of the recordings. This can be formulated as follows: We are given samples of an audio segment, xk, k = 0,..., N-1, and wish to fit a model of the form, L Tkacos (ek) + be sin(ek), l=1 (2) where L are a number of tones present in the audio segment; e are the tonal frequencies and a and be are the coefficients. (a) Show that if the frequencies are given, we can solve for the coefficients ae and be using linear regression. Specifically, rewrite the model (2) as x A for appropriate x, A and 3. Then describe exactly how we obtain the coefficients a and be from this model. (b) Now suppose the frequencies were not known. If we had to solve for the parameters ae, be and e, would the problem be a linear regression problem? 5. In audio processing, one often wants to find tonal sounds in segments of the recordings. This can be formulated as follows: We are given samples of an audio segment, xk, k = 0,..., N-1, and wish to fit a model of the form, L Tkacos (ek) + be sin(ek), l=1 (2) where L are a number of tones present in the audio segment; e are the tonal frequencies and a and be are the coefficients. (a) Show that if the frequencies are given, we can solve for the coefficients ae and be using linear regression. Specifically, rewrite the model (2) as x A for appropriate x, A and 3. Then describe exactly how we obtain the coefficients a and be from this model. (b) Now suppose the frequencies were not known. If we had to solve for the parameters ae, be and e, would the problem be a linear regression problem?