Husheng Li, UTK-EECS, Fall 2012

 An ideal low pass filter can be used to obtain the exact original signal.

 We can use C/D converter to convert a continuous-time signal to a discrete-time one, process it in a discrete-time system, and then convert it back to continuous time domain.

 We can use a discrete-time low pass filter (LPF) to do the low pass filtering for continuous time signal.

 The ideal low pass discrete-time filter with discrete-time cutoff frequency w has the effect of an ideal low pass filter with cutoff frequency w/T.

 We can also use continuous-time system to process discrete-time signals.

With aliasing Without aliasing

 A general system for downsampling by a factor of M is the one shown above, which is called a decimator.

 The change of sampling rate by a non-integer factor can be realized by the cascade of interpolator and decimator.

 Multirate techniques refer in general to utilizing upsampling, downsampling, compressors and expanders in a variety of ways to improve the efficiency of signal processing systems.

 The operations of linear filtering and downsampling / upsampling can be exchanged if we modify the linear filter.

 The two stage implementation is often much more efficient than a single-stage implementation.  The same multistage principles can also be applied to interpolation

 In practice, continuous time signals are not precisely band limited, ideal filters cannot be realized, ideal C/D and D/C converters can only be approximated by A/D and D/A converters.

 We can use oversampled A/D to simplify the continuous-time antialiasing filter.

 Key point: the noise is aliased; but the signal is not. Then, the noise can be removed using a sharp-cutoff decimation filter.

 This quantizer is suitable for bipolar signals.  Generally, the number of quantization levels should be a power of tow, but the number is usually much larger than 8.

 Oversampling can make it possible to implement sharp cutoff antialiasing filtering by incorporating digital filtering and decimation.  Oversampling and subsequent discrete-time filtering and downsampling also permit an increase in the step size of the quantizer, or equivalently, a reduction in the number of bits required in the A/D conversion.