Consider the sinusoidal signal generator in Fig. P6.23, where both the stored sinu-soida...

Consider the sinusoidal signal generator in Fig. P6.23, where both the stored sinu-soidal data

and the sampling frequency are fixed. An engineer wishing to produce a sinusoid with period 2N suggests that we use either zero-order or first-order (linear) interpolation to double the number of samples per period in the original sinusoid as illustrated in Fig. P6.23(a).

(a) Determine the signal sequences y(n) generated using zero-order interpolation and linear interpolation and then compute the total harmonic distortion (THD) in each case for N = 32, 64, 128.

(b) Repeat part (a) assuming that all sample values are quantized to 8 bits.

(c) Show that the interpolated signal sequences y(n) can be obtained by the system shown in Fig. P6.23(b). The first module inserts one zero sample between successive samples of x(n). Determine the system H(z) and sketch its magnitude response for the zero-order interpolation and for the linear interpolation cases. Can you explain the difference in performance in terms of the frequency response functions?

(d) Determine and sketch the spectra of the resulting sinusoids in each case both analytically [using the results in part (c)] and evaluating the DFT of the resulting signals.

(e) Sketch the spectra of and y(n), if x(n) has the spectrum shown in Fig. P6.23(c) for both zero order and linear interpolation. Can you suggest a better choice for H(z)?