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In a practical implementation of the frequency sampling realization, quantization effects preclude a perfect cancellation of the poles and zeros.
  • a)
    True
  • b)
    False
Correct answer is option 'A'. Can you explain this answer?
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In a practical implementation of the frequency sampling realization, q...
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.
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In a practical implementation of the frequency sampling realization, q...
Introduction:
The frequency sampling technique is a method used for the design of digital filters. It involves sampling the desired frequency response of the filter and then obtaining the filter coefficients by taking the inverse discrete Fourier transform (IDFT) of the sampled frequency response. The resulting filter coefficients are used to implement the filter.

Quantization Effects:
Quantization is the process of representing continuous values with a limited number of discrete values. In the context of digital filters, quantization refers to the process of representing the filter coefficients with a limited number of bits.

Perfect Cancellation of Poles and Zeros:
In an ideal scenario, the frequency sampling technique would allow for a perfect cancellation of the poles and zeros of the filter. This means that the resulting filter would have a frequency response that exactly matches the desired frequency response.

Quantization Effects on Poles and Zeros:
However, in a practical implementation of the frequency sampling technique, quantization effects come into play. When the filter coefficients are quantized, the accuracy of the representation is compromised. This can lead to errors in the cancellation of the poles and zeros of the filter.

Reasons for Quantization Effects:
There are several reasons why quantization effects occur in the frequency sampling technique:
1. Limited number of bits: The filter coefficients are represented using a limited number of bits. This introduces quantization errors, as the exact values of the filter coefficients cannot be represented.
2. Round-off errors: The quantization process involves rounding off the filter coefficients to the nearest representable value. This rounding off introduces errors in the filter coefficients.
3. Truncation errors: In some cases, the filter coefficients may need to be truncated to fit within the limited number of bits. This truncation can lead to errors in the filter coefficients.

Impact of Quantization Effects:
The quantization effects can have a significant impact on the performance of the filter. The errors introduced by quantization can distort the frequency response of the filter, causing deviations from the desired response. These deviations can affect the filter's ability to accurately process the input signal.

Conclusion:
In conclusion, the practical implementation of the frequency sampling technique is affected by quantization effects, which prevent a perfect cancellation of the poles and zeros of the filter. These quantization effects introduce errors in the filter coefficients, leading to deviations from the desired frequency response. It is important to consider these quantization effects and their impact on the filter performance when designing and implementing digital filters using the frequency sampling technique.
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In a practical implementation of the frequency sampling realization, quantization effects preclude a perfect cancellation of the poles and zeros.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?
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