## Thursday, 26 December 2013

### SIGNALS & SYSTEMS

SIGNALS & SYSTEMS
1.      The Fourier series of an odd periodic function contains only Sine terms.
2.      The Fourier transform of a real valued time signal has Conjugate symmetry.
3.      If a signal f(t) has energy E, the energy of the signal f(2t) is equal to E/2.
4.      The Laplace transform of a unit ramp function starting at t=a, is / .
5.      The z-transform f(z) of the function f(nT)=  is z/z- .
6.      The transfer function of a linear system is a Ratio of the Laplace transform of the output and that of the input with all initial conditions zero.
7.      A system with an input x(t) and an output y(t) is described by the relation:
y(t)=t x(t).this system is linear and time varying.
8.      A system is defined by its impulse response h(n)= u(n-2). The system is Causal but not stable.
9.      A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is a Triangular pulse.
10.  Increased pulse-width in the flat-top sampling, leads to Attenuation of high frequencies in reproduction.
11.  Flat top sampling of low pass signals gives rise to aperture effect.
12.  A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through an ideal low-pass filter with the appropriate bandwidth.
13.  The ACF of a rectangular pulse of duration T is a triangular pulse of duration 2T.
14.  The system has one or more outputs is called response.
15.  Flattop sampling uses sample and hold circuit.
16.  Fourier series used to analyze Periodic signals.

17.  When the high frequency interferes with low frequency and appears as low frequency then it is called aliasing.