SIGN Flashcards
signal
A signal is a function representing a physical quantity or variable. Typically it contains information about the behaviour or nature of the
phenomenon.
signal processing
In signal processing we try to translate a system or a signal into
mathematics. The goal of signal processing is to replace complex signals with simpler ones we understand (decomposition).
Continuous signal
- Signal x (t)
- t is a continuous variable
Discrete signal
- Signal x[n]
- t is a discrete time variable
Periodic
A continuous-time signal is said to be periodic with period T if there is a positive nonzero value of T
System
A system is a mathematical model of a physical process that relates an input (or excitation) signal to an output (or response) signal.
Impulse decomposition
Impulse decomposition provides a way to analyse signals one sample at a time.
Impulse response
The impulse response is the signal that exits a system when a delta function (unit impulse) is the input.
Impulse stappenplan
1) The input signal can be decomposed into a set of impulses, each of which can be viewed as a scaled and shifted delta function.
2) The output resulting from each impulse is a scaled and shifted version of the impulse response.
3) The overall output signal can be found by adding these scaled and shifted impulse responses
Convolution
Convolution is a formal mathematical operation, just as multiplication, addition, and integration. Addition takes two numbers and produces a third number, while convolution takes two signals and produces a third signal
Input side algorithm
analysing how each sample in the input signal contributes to many points in the output signal
Output side algorithm
ooking at individual samples in the output signal, and finding the contributing points from the input
Properties convolution
Cummutative
Associative
Distributive
A set of weighing coefficients
each sample in the output signal is equal to a sum of weighted inputs
Propreties of LTI systems
- Memory(less)
- Causality
- Linearity
- Time-invariant
- Memory(less)
A system is said to be memoryless if the output at any time depends only on the input at the same time. Otherwise, the system is said to have memory. Examples of systems with memory, are systems described with an integral or sum;
- Causality
A system is said to be causal if its output at the present time depends on only the present and/or
past values of the input. Thus, in a causal system, it is not possible to obtain an output before an
input is applied to the system. A system is called non-causal if its output at the present time depends
on future values of the input. Note that all memoryless systems are causal, but not vice versa.
- Linearity
A system is linear if it satisfies the superposition property
- Time-invariant
A system is called time-invariant if a time shift (delay or advance) in the input signal causes the same time shift in the output signal.
Fourier Series
any periodic signal could be expressed as a sum of sinusoids
Sinusoidal fidelity
If the input to a linear system is a sinusoidal wave, the output will also be a sinusoidal wave, and at exactly the same frequency as the input.
Discrete Fourier Transformaties
The Fast Fourier Transform, a fast algorithm for computing the Discrete Fourier Transform, is used commonly in engineering applications where the signal processing of measured data is performed.
Fourier series soorten
- Complex fourier
- Trigometric fourier series (real fourier series)
- Harmonic form fourier series
