Digital System Processing

These are: Delay: Shift towards Right Advance: Shift towards Left Folding: Reversing in x-direction Scaling: scaling factor>1: for eg. y(n)=x(kn) where k>1: so we will remove k-1 samples from between two samples scaling factor<1: for eg. y(n)=x(n/k) where k>1: so we will add k-1 samples of nil value in between two samples x(n)=Acos(2pi f1 n)+ sin(2pi f2 n)+ cos(2pi f3 n), how to find its period? Take LCM of all the periods n1,n2 and n3

Basic Signals Impulse Signals Unit Step Signal Ramp Signal Exponential Classification of Discrete Time Signals Energy & Power Signals: E(n)=Summation from -inf to +inf (|x(n)^2|);  P(n)=(Summation from -inf to +inf (|x(n)^2|))/(2N+1) If the signal is periodic with period N, then: P(n)=(Summation from 0 to n=N-1 (|x(n)^2|))/N Aperiodic signals are generally Energy Signals whereas Periodic ones are Power Signal Periodic and Aperiodic Signals:  x(n)=x(n+N), so if x(n)=Acos(2*pi*f*n) So, x(n+N)=Acos(2*pi*f*(n+N))= Acos(2*pi*f*n+2*pi*f*N) Now 2*pi*f*N=2*pi*K so f=K/N (K & N are integers) A signal is periodic only if the normalized frequency is a rational number that is K/N otherwise the signal is not periodic. All continuous time sinusoidal are periodic whereas all discrete time sinusoidal are not periodic. Even and Odd Signal Symmetric: x(n)=x(-n) Antisymmetric: x(n)=-x(n) Even part: xe= (x(n)+x(-n))/2 Odd part: xe= (x(n)-x(-n))/2

There are two kinds of Analog signals: Continuous and Discrete What is Sample & Hold? When in a discrete signalling, the value of signal is selected after each interval of time, then that interval of time is known as sampling interval. And such a circuit which enables us to do so is called the Sample and hold circuit. We are getting the value of the signal at every interval, which is integral multiple of sampling interval (T). A digital signal is discrete in space as well as time.- Quantization: Discreetness in Amplitude as well as Time . Hence, every continuous time signal is an analog signal but every analog signal is not continuous time signal. We need to remove abrupt change and to remove them we need to improve the higher frequencies (which have infinite harmonics). That is why we pass it through low pass filter . Advantages of DSP Less Sensitivity: In case of analog, noise remains in the signal but in digital, it is less sensitive. For eg. if V=5V ...