. 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, xk ? X L `=1 a` cos(?`k) + b` sin(?`k), (2) where L are a number of tones present in the audio segment; ?` are the tonal frequencies and a` and b` are the coefficients. (a) Show that if the frequencies ?` are given, we can solve for the coefficients a` and b` using linear regression. Specifically, rewrite the model (2) as x ? A? for appropriate x, A and ?. Then describe exactly how we obtain the coefficients a` and b` from this model. (b) Now suppose the frequencies ?` were not known. If we had to solve for the parameters a` , b` and ?` , would the problem be a linear regression problem?

5. In audio processing, one often wants to nd tonal sounds in segments of the recordings. This can be formulated as follows: We are given samples of an audio segment, 3;\" R: = U. . . . . N 1., and wish to t a model of the form, L 1,. m Zogcos[gk) + a? 3511mm), (2] =l where L are a number of tones present in the audio segment; g are the tonal frequencies and GE and bf are the coefcients. (a) Show that if the frequencies f are given, we can solve for the coefcients a; and fig using Linear regression. Specically, rewrite the model (2) as x F: AB for appropriate x, A and ,6. Then describe exactly how we obtain the coefficients {If and g from this model. (b) Now suppose the frequencies g were not known. If we had to solve for the parameters f, fig and g, would the problem be a linear regression