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Discuss Fourier Transform and what effects multiplying a time domain signal by a sinusoid (including multiple...

Discuss Fourier Transform and what effects multiplying a time domain signal by a sinusoid (including multiple times) has on both the time and frequency domain representations, as well as the practical use of the method. No more than 300 Words.

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Answer #1

The FT decomposes a function of time into the frequencies.

The Fourier transform if a function of time itself is a complex valued function of frequency whose absolute value represents the amount of that frequency present in the original function and whose complex augment is the phase offset of the basic sinusoidal in that frequency.

The Fourier transform is extension of Fourier series that results when the period of the represented function is lengthened and allowed to approach infinity.

Due to properties of sine and cosine it is possible to recover the amplitude of each wave in a Fourier series using an integral

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