倕楔潭桴匠档-Lecture2ContinuationofSampling.ppt

10-Sept., 1998 EE421, Lecture 2 Lecture 2: Continuation of Sampling Butterworth FiltersThe frequency response magnitude for an Nth order Butterworth filter is of the form: The cutoff frequency is f0. The roll-off rate is 20N dB/decade. Butterworth Filters 2nd order Sallen-Key low-pass filter (can be cascaded to create 4th, 6th, 8th, … order filters) Butterworth Filters Example 2.1: Suppose H0 = 1 and you want to select f0 for 1 dB (or less) attenuation over the band from 0 to 4 kHz.at f = 4 kHz. So,or Ideal Reconstruction Ideal Reconstruction The impulse response of an ideal reconstructor is a sinc function, therefore an ideal reconstructor uses sinc interpolation. Practical Reconstruction The staircase reconstructor is the simplest and most widely used reconstructor in practice. Basically, it is a sample and hold. Staircase Reconstruction Staircase Reconstruction The staircase reconstructor should be followed by a low-pass filter to remove the residual images. Also, a staircase reconstructor suffers from nonuniform pass-band attenuation. This can be corrected with a digital equalization filter with a response equal to an inverse sinc function over the pass-band. * EE421, Fall 1998 Michigan Technological University Timothy J. Schulz * C C R R (1-K)Rf Rf + - + + - - input output in kHz signal spectrum sampled-signal spectrum ideal reconstruction filter Reconstructed-signal spectrum f f f sampled signal Interpolation signals Interpolated signal sampled signal Interpolation signals Interpolated signal The impulse response for a staircase reconstructor is a rectangle. Therefore, its frequency response is a sinc! signal spectrum staircase reconstruction filter Reconstructed-signal spectrum f f f sampled-signal spectrum surviving replicas (images)