# Solution Library

# Interpolation Techniques to Interpolate the Subsequences

**Question**

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

- 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

- 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* xÍ‚(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

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