Signals and Systems Flashcards
(15 cards)
Comparing ECG, EEG, EMG, which signal is closest to a deterministic signal and Why?
ECG as it is the most regular, with clearly defined morphology in contrast to EEG and EMG signals which may show regularity in very short term periods.
Define a unit sample sequence and explain how an arbitray signal be presented using the sequence
An arbitrary digital signal can be presented as a weighted sum of unit sample sequences (also equation)
The amplitude of a digital signal is in a rnage of 0-3. If quantisation is 0.25, how many different values of amplitude can the signal have?
13, 0,0.25,0.5,…2.75,3
What is the quantisation of a digital signal?
Quantisation shows how precisely it is possible to define the amplitude of a signal, smaller quantisation means smaller difference between two values of amplitude i.e larger precision
What is Ailiasing
Effect when signal reconstruction from a digital signal is different from the original signal. Higher Frequencies get mirrored in the lower frequency domain.
Expplain Shannon-Nyquist theorem
Sampling frequency (fs=1/Ts) must be at least 2X greater than the highest frequency fc of the continuous signal x(t). The highest frequency that can be reconstructed from the signal fs is called Nyquist Frequency. If sampling frequency is not high enough the frequency content of the signal is distorted due to aliasing.
What is zero padding and where is it used
2 main applications, 1: adding zeros to a signal to achieve a length of 2^n to be able to apply FFT, which reduces the number of numerical operations required for DFT. Because of the numerical procedure which requires half the sequence in time or in frequency domain the duration of sequence must be 2^n.
2: To increase the overall duration of a sequence and to provide interpolation of a frequency between x(k) & x(k+1). This can be useful to e.g. precisely determine location of an isolate peak. This process however does not improve the resolution of a signal in frequency domain. The only way to improve this would be to increase the sampling rate of the signal in Time domain.
What is the relation between multiplication & convolution in time & frequency domain in DFT
Multiplication in time corresponds to convolution in frequency
For which types of signal is STFT used? What assumption do we make when using STFT?
STFT is used for dynamic signals which change over time. We assume that the signal is stationary within a window in which STFT is applied.
How do we create STFT?
Instead of applying one wondow function over the whole period Ts in which we want to analyse X(t) we apply a set of smaller windows, which are typically overlapping for 50% to avoid the edge aliasing effect. In this was we can analyse how time-frequency distribution changes over time.
What is the main problem with time and frequency resolution in STFT
Small time windows give a better time resolution but poorer frequency resolution and vice versa.
What is the energy spectrum density?
Shows how the energy of a signal is distributed over frequency. Makes most sense when energy is finite. Can be summed over all frequencies to give total energy.
What is Power Spectrum Energy (PSD)
Obtained when the energy spectral density is divided by a finite time period in which a signal was measured
Explain the steps of the wlesh period gram to calculate PSD
Signal is devided into smaller segments overlapping by 50%
- Each segment is multiplied with a window function in time domain
- FFT of each window segment is calculated
- Results are averaged over different time windows
what is the difference between correlation and convolution
Correlation is measurement of similarity between two signals
Convolution is measurement of effect of one signal on the other signal
