Question

Q) explain the basic Meaning of the followings:

Filters and types,

modulation md demodulation

difference btwm AM and FM,

Fourier, laplace and z transform ?

which technology is better

Q)fourier series and its need?

Q)Why we do convolution

Answer 1

Filter:

Sometimes it is needed to have circuits that are capable of selectively filtering a particular frequency or range of frequencies from a mixture of various frequencies. An electrical circuit or an arrangement of devices designed to perform this task is called a filter.

There are four primary types of filters which are:

low-pass filter (filters out high frequencies)

high-pass filter (filters out Low frequencies)

band-pass filter (filters out low and high frequencies and passes a band of desired frequencies )

notch filter (also called band-reject or band-stop filter) (filters out only a band of selected frequencies and pass the rest)

Modulation:

Modulation is the process of changing the characteristics of the carrier signal based on the message / modulating signal's characteristics such as the frequency, Phase or Amplitude etc. Modulation process enables the message signal to be carried over large distances.

Demodulation:

Demodulation or detection is the process of extraction of original message signal from the modulated carrier signal.

AM and FM:

In AM, the carrier wave frequency is continuously changed as a function of Amplitude of the message signal whereas in FM, the carrier wave Amplitude is continuously changed as a function of Amplitude of the message signal.

Fourier, Laplace and Z transform:

Fourier transform is the transform from time domain information to frequency domain information. This transform is usually applied to time domain signals to find out the frequency content that it has. i.e. what frequency components that the signal contains. In essence, the Fourier transform is another way of looking at a signal. Fourier Transform can be applied to systems as well that satisfy Dirichlet's conditions for convergence.

Laplace transform is also for converting time domain representation of a signal or system to complex variable representation (in terms of complex variable 's'). All systems that can be represented with Laplace transform may not have the Fourier transform. This is because of the fact that the Region of convergence of Laplace transform is much larger than that of the Fourier transform. In finding a Laplace transform if the ROC contains the JW axis, then the system will have a Fourier transform. In essence, we can think of the Fourier transform as a special case of Laplace transform with the ROC mapped onto the JW axis.

In contrast to continuous signals, the Z transform is only applicable for discrete time signals. The  Z transform in the discrete domain is analogous to Laplace in the continuous domain.

Fourier series and its need:

Fourier series is the representation of any signal that satisfies the Dirichlet's conditions in the form of summation of sinusoids or complex exponentials with integer multiples of fundamental frequencies of the given signal.'

For the series transform to be applied, the signal first needs to be in the period form.

With the help of fourier series, one can represent the periodic functions as a weighted sum of sinusoids. as a result we can easily identify the what frequency content the signal has and what dominant frequencies are present in the signal. etc.

Convolution:

In linear systems, convolution is used to describe the relationship between three signals of interest: the input signal, the impulse response, and the output signal. The output signal is nothing but the convolution os input and impulse response. A system can be represented as a signal by finding it's impulse response. convolving it with the input to the system gives the output in the same domain(i.e. time domain).Convolution applicable for the linear system only.