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How to quantize the transfer function of a digital filter?
Let a digital filter’s ideal transfer function be H 1 If the ‘s and ‘s are quantized, the poles and zeros move, creating a new transfer function N k k k N k k k bz z az ab ()0 1 ˆ Hˆ 1 ˆ where ˆ and ˆ . N k k k N k k k kkkkkk bz z az aaabbb Quantization of Filter Coefficients 1 1 1 1 1
How is the quantization of filter coefficients minimized?
The corresponding change in the frequency response can be minimized by realizing a filter with a large number of poles and zeros as an interconnection of second-order sections. That is, the physical realization of these filters can be done in a particular manner that reduced the effect of the quantization of filter coefficients.
How many bits are in a filter coefficient?
Filter coefficients are represented by a finite number of bits, commonly in the range of 8 to 16 bits. This results in the implementation of a filter that differs slightly from the original design.
How to quantize the poles of a filter?
Let’s quantize the coefficients by truncating them to 3-bits. The new poles are at P1′ = 2.625 and P2′ = 0.625 Thus we can see a huge shift in the position of the poles. In the cascade realization method, the transfer function can be written as follows: H (z) = H1 (z) . H2 (z) Let’s quantize the coefficients by truncating them to 3-bits.
How are the values of the filter coefficients quantized?
But since we are quantizing the values of the filter coefficients to fit them into the register, there will be a change in the values of the poles and zeros. This, in turn, causes the location of the poles and zeros to shift from the desired location.
What are the magnitude and phase characteristics of the all-pass filter?
The magnitude and phase characteristics are described by: The conventional all-pass filter exists only at α = 1, as depicted in Fig. 7. However, the magnitude response has a minimum for α < 1 and a maximum when α > 1, as depicted in Fig. 7.
Is there a maximum for an all pass filter?
The conventional all-pass filter exists only at α = 1, as depicted in Fig. 7. However, the magnitude response has a minimum for α < 1 and a maximum when α > 1, as depicted in Fig. 7. Fig. 7. Numerical simulation for the FAPF for different α.