Aliasing Down-sampling by a factor of M^th, in itself, is simply retaining every M sample while dropping all samples in between. If, therefore, prior to down-sampling, the signal x(n) is indeed band-limited to π/M then we generate the down-sampled version y(n) by simply taking every M^th sample of x(n). This process is shown below in block diagram fashion. If in this set-up x(n) is not band-limited as required then the spectrum of y(n) will contain overlapping spectral components of x(n) due to stretching, i.e., X (w / M ) will overlap X (w- 2p / M ), etc. This results in aliasing.

Band-limiting x(n) to π/M (if not done already) is done by an anti-aliasing filter (digital low pass filter) with a cut-off frequency of π/M. The general process of decimation then consists of filtering followed by down sampling shown in block diagram below.

Unlike an analog anti-aliasing filter associated with an ADC, the filter in this diagram is a digital anti-aliasing filter specified as

Note that π corresponds to F_x/2 and π/M corresponds to F_x/2M where Fx is the sampling frequency of x(n).

Typically, in order to avoid (delay) distortion, the filter H(z) is a linear phase FIR filter with (N+1) coefficients {h(r), r = 0 to N}. The output, v(n), of the low pass filter is then given by convolution

and the decimated signal is

In summary, in order to down sample a signal by a factor of M:

• The signal should have been originally over-sampled by a factor of M (that is originally band limited to π/M and over-sampled). In this case the signal is down- sampled straightaway; no pre-filter is needed. OR

• The signal, assumed originally band limited to π, should be band-limited to π/M by a pre-filter; the signal is then down-sampled. In this case there will be some loss of information.

Email based Aliasing assignment help - Aliasing homework help at Expertsmind

Are you finding answers for Aliasing based questions? Ask Aliasing questions and get answers from qualified and experienced  Digital signal processing tutors anytime from anywhere 24x7. We at www.expertsmind.com offer Aliasing assignment help -Aliasing homework help and  Digital signal processing  problem's solution with step by step procedure.

Why Expertsmind for Digital signal processing assignment help service

1.     higher degree holder and experienced tutors

2.     Punctuality and responsibility of work

3.     Quality solution with 100% plagiarism free answers

4.     On Time Delivery

5.     Privacy of information and details

6.     Excellence in solving Digital signal processing queries in excels and word format.

7.     Best tutoring assistance 24x7 hours