What is the basic concept of Fourier theory as it relates to real-world signals? How does the transfer function of a filter relate to this concept?

2) Describe: a) various types of Signals, b) The idea behind Fourier Transform, c) Analog to Digital Conversion, Nyquist Sampling Theorem, d) Errors associated with A to D conversion that are related to Nyquist Sampling Theorem.

given a descrete signal x[n]={...0,10,8,6,4,2,0,...} find even component and odd component

The CT signal x(t)=6cos (800πt) + 8cos2(mπt) is critically sampled (Nyquist rate) by fs=8000 Hz. Find: i. The value of m. ii. The frequency components of the signal. iii. The frequency resolution (∆f) of the output spectrum if the sampled signal is processed by 32point-DFT. iv. Define frequency resolution