## Determine the DFT of y=32 sin 5 (2πft) where f =30Hz.Use 512 points sampled over 1second.

Determine the real and imaginary parts of the DFT, using the MATLAB function fft, for the followingperiodicdatawherethe32datapointsaresampledatintervalsof0.1second.Examine the amplitude and frequency of its components. What conclusions can you draw from these results?

y=[2 −0.404 0.2346 2.6687 −1.4142 −1.0973 0.8478 −2.37 0 2.37 −0.8478 1.0973 1.4142 −2.6687 −0.2346 0.404 −2 1.8182 1.7654 −1.2545 1.4142 −0.3169 −2.8478 0.9558 0 −0.9558 2.8478 0.3169 −1.4142 1.2545 −1.7654 −1.8182]

Determine the DFT of y=32 sin 5 (2πft) where f =30Hz.Use 512 points sampled over 1second. From the imaginary part of the DFT estimate the coefﬁcients a0, a1, a2 in the relationship

32sin5(2πft)=a0sin[2πft]+a1sin[2π(3f)t]+a2sin[2π(5f)t]

Repeat the process for y=32 sin 6 (2πft) where f =30Hz.Use512pointssampledover1second. From the real part of the DFT, estimate the coefﬁcients b0, b1, b2, b3 in the relationship

32sin6(2πft)=b0+b1cos[2π(2f)t]+b2cos[2π(4f)t]+b3cos[2π(6f)t]

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