Test: Frequency Sampling Method FOR Design - Electronics and Communication Engineering (ECE) MCQ

Explanation: In the frequency sampling method, we specify the frequency response Hd(ω) at a set of equally spaced frequencies, namely

Explanation: To reduce the side lobes, it is desirable to optimize the frequency specification in the transition band of the filter. This optimization can be accomplished numerically on a digital computer by means of linear programming techniques.

Explanation: The desired output of an FIR filter with an input h(n) and using a window of length M is given as

Explanation: Since {h(n)} is real, we can easily show that the frequency samples {H(k+α)} satisfy the symmetry condition
H(k+α)= H*(M-k-α).

Explanation: The symmetry condition, along with the symmetry conditions for {h(n)}, can be used to reduce the frequency specifications from M points to (M+1)/2 points for M odd and M/2 for M even. Thus the linear equations for determining {h(n)} from {H(k+α)} are considerably simplified.

Explanation: Although the frequency sampling method provides us with another means for designing linear phase FIR filters, its major advantage lies in the efficient frequency sampling structure, which is obtained when most of the frequency samples are zero.

Explanation: There is a potential problem for frequency sampling realization of the FIR linear phase filter. The frequency sampling realization of the FIR filter introduces poles and zeros at equally spaced points on the unit circle.

Explanation: In the ideal situation, the zeros cancel the poles and, consequently, the actual zeros of the H(z) are determined by the selection of the frequency samples H(k+α). In a practical implementation of the frequency sampling realization, however, quantization effects preclude a perfect cancellation of the poles and zeros.

Explanation: According to the frequency sampling method for FIR filter design, the desired frequency response is specified at a set of equally spaced frequencies.

Explanation: To reduce side lobes, it is desirable to optimize the frequency specification in the transition band of the filter.