Interpolation Techniques to Interpolate the Subsequences

Question

Below, two data sequences were used for the interpolation experiments.

1. Consider a simple single-mode 128-point sequence

x(n) = sin(πn/64)                        for    n = 0, 1, … 127

The 32-point subsequence corresponding to a lower sampling rate is in the form of

xÍ‚(n) = sin(πn/16)                        for    n = 0, 1, … 31

Use FFT method to interpolate the subsequence xÍ‚(n) to 128 points. Plot the resultant 128-point sequence: it shows  below

2. Consider the 64-point sequence

x(n) = 2^(-n/16)                             for    n = 0, 1, … 63

The 32-point subsequence corresponding to a lower sampling rate is in the form of

xÍ‚(n) = 2^(-n/8)                                 for    n = 0, 1, … 31

Use FFT method to interpolate the subsequence x͂(n) to 64 points. Plot the resultant 64-point sequence: it shows below

Answer the question: Does the interpolation technique work equally well for both sequences? Explain why so.

Summary: This question belongs to Fourier series in engineering mathematics and discusses about interpolation techniques to interpolate the subsequences.

Total word count: 203