In the Goertzel algorithm for computation of the discrete Fourier transform, X[k] is computed as X[k] =
Question:
In the Goertzel algorithm for computation of the discrete Fourier transform, X[k] is computed as X[k] = Yk[n], where yk[n] is the output of the network shown in Figure. Consider the implementation of the Goertzel algorithm using fixed-point arithmetic with rounding. Assume that the register length is B bits plus the sign, and assume that the products are rounded before additions. Also, assume that round-off noise sources are independent.
(a) Assuming that x[n] is real, draw a flow graph of the linear ?noise model for the finite-precision computation of the real and imaginary parts of x[k]. Assume that multiplication by ? 1 produces no round-off noise.
(b) Compute the variance of the round-off noise t=in both the real part and the imaginary part of X[n].
Step by Step Answer:
Discrete Time Signal Processing
ISBN: 978-0137549207
2nd Edition
Authors: Alan V. Oppenheim, Rolan W. Schafer