Digital Signal Processing

Continous: Define  each instant of time
Discrete: define particular instant of time only i.e. discontinous in time axis and continous in amplitude axis
Analog: both time and amplitude are continous
Digital : both time and amplitude are dis-continous

-Continious vs Discrete (Time Axis)
-Digital vs Discrete (Amplitude Axis)
-Analog Vs Digital  
-Continious Vs Analog (Time vs Both Time & amplitude continous)
-Amplifier vs Attenuator
-Signum Function
-Rectangular Function/Gate function

-Signal
  Types of Signal
-ADC
   Sampling (Nyquist)
   Quantization
-System
   Types of System
-LTI System
   Convolution
   Impulse Response
   Eigen Function (Base fun{eg: exponential sinusiodal}:To shift from convolution to multiplications) & Eigen Value (Transfer function)
-Transforms
   CT Fourier Series    [input: CT, P :::: Output: DT, NP] [Represent any general signal in form of base function]
   DT Fourier Series    [input: DT, P :::: Output: DT, P]
   CT Fourier Transform [input: CT, NP :::: Output: CT, NP]  [Magnitude Spectrum: Even, Phase Spectrum: Odd] [For energy, stable signal]
   DTFT                 [input: DT, NP :::: Output: CT, P] [For infinite sequence] 
   DFT  [N ponit DFT]  		
	[input: DT, P :::: Output: DT, P]  [For finite sequence ie N points, ie sampling one period of DTFT] [Allow to evaluate FT on digital 		computer] [Linear Convolution, Circular Convolution] [N*N Multiplication, N(N-1) addition]
   FFT [Not a transform, reduce computation, N/2logN mul , NlogN add, Radix r FFT, Butterflies N/2]
   Laplace Transform:
	 [Generalization of CTFT, For both stable and unstable] [Freq. domain not visible, for designing system] [Unilateral [Causal, initial 			condition], Bilateral (ROC)] [Does n't exist for periodic signal]
   Z-Transform 
	 [Genralization of DTFT, counter part of discrete LT, All analog TF mapped to discrete TF, map infinite analog freq. to {0,2pi},ROC (Unit cicle)]

-Filters
   LPF
   HPF
   BPF
   BRF

-Digital Filters
   IIR (magnitude response, feedback, Unstable,  depends upon present input as well as past outputs,)
   FIR (Stable, Depends on present input and past input, no feedback,  Linear phase response, eg:  )

-Types of Windows function
   Rectangular
   Hamming
   Hanning
   Bartlett
   Kaisar

Rayeilgh/Parseval Power Relation
Weiner Kincheir Relation
Center Ordinate Theorm
Drichlet Conditions
Gibbs Phenomenon


Analog----> Sampler >>>>> Discrete ------> Quantizer --------> Encoder>>>>>>>>>> Digital
Convolution is a mathematical operation which is used to expressed the i|p and o|p relationship in LTI system.
Fourier Series: To represent any point/vector in space we require base co-ordinate x,y,z vector, In same case to represent any general signal we require base signal set. 
Eg: sinwt, coswt, sinusoidal exponential,(orthogonality is must)


Distortionless System:
Constant magnitude response and linear phase response.
Bandwith for distortionless system is infinite.

Bandwidth: Width of group of frequencies for which magnitude response of an LTI system is non-zero.