1) An ideal low pass rectangular filter has an oscillation (e.g., ripples) near
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Question
1) An ideal low pass rectangular filter has an oscillation (e.g., ripples) near the cut off frequency, which is referred to as the Gibb’s phenomenon. Gibb’s phenomenon is persistent independent of the sampling frequency. True or false
2) Hamming window can provide an approximation of an ideal rectangular filter at the cost of reducing the transition band while decreasing the ripples in the stop band. True or false
3) The number of coefficients for an FIR filter are usually smaller than an IIR filter. True or false
Explanation / Answer
1). This statement is True. An ideal low pass rectangular filter has an oscillation near the cut off frequency, which is referred to as the Gibb’s phenomenon.Gibbs phenomenon can be ameliorated by using a smoother method of Fourier series summation Gibb’s phenomenon is persistent independent of the sampling frequency.The Gibbs phenomenon is also closely related to the principle that the decay of the Fourier coefficients of a function at infinity is controlled by the smoothness of that function; very smooth functions will have very rapidly decaying Fourier coefficients, whereas discontinuous functions will have very slowly decaying Fourier coefficients
2). This statement is True. Hamming window can provide an approximation of an ideal rectangular filter at the cost of reducing the transition band while decreasing the ripples in the stop band. The large amount of ripple visible on the non-dB plot is due to the rather crude approach of truncating the infinite ideal impulse response. The approach that has just been used is called applying a Rectangular Window.
3). This statement is False.IIR filters require fewer coefficients than FIR filtersto execute similar filtering operations.
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