Spectral Analysis and Time Frequency analysis Flashcards
What is Continuous Fourier Transformation (CFT)?
Matching between the original signal x (t) and the complex exponential signal (sine and cosine function) of different frequencies
Fast Fourier Transformation (FFT)?
Predicts that the signal is periodic and will be repeated over time
Trade off between frequency resolution and spectral leakage
Many different windows
What is windowing?
A method to reduce spectral leakage
What is Welch periodogram?
Not a consistent estimate of the power spectrum - variance does not approach zero with data length
Higher variability for larger data sets
Averaging the periodogram; reduced variability and statically consistent; availability of confidence intervals and error bars
What are some characteristics of time-frequency representations?
No spectral information in the time domain representation
No temporal information in the frequency domain representation
A time-frequency representation of a signal provides some temporal and some spectral information
Trade off between specificity in time and specificity in frequency
All time information is lost in the frequency domain
There may be an event related increase in amplitude for certain frequency and therefore amplitude and phase are not consistent over time
Cannot use frequencies that are slower than the epochs
Cannot study above the Nyquist frequency
Cannot differentiate two closely spaced frequencies
What is TRF analysis?
TRF signal is obtained by calculating a moving average (complex concolution) of the similarity between wavelength and this signal
What frequency bands to consider in TRF?
Depends on test, findings and lengths of trials and data epoch
Show activity a bit above and below the predicted frequency band
If no prediction use a standard frequency band 40-60Hz
Lowest frequency depends on the trial lengths and the highest on the sampling rate
How many frequencies to choose in TRF?
More frequencies to help data exploration and to select appropriate frequency ranges
But bigger data matrix and computational time, multiple comparison problem and correlated values
Usually 25-30 Frequencies
What would be the frequency spacing in TRF?
linear or logarithmic scale
Not mush effort on statistical analysis but visual
High frequency findings - linear scale visual
low frequency finding - log scale visual
How many cycles in TRF?
Trade off between temporal and frequency precision - large number of cycles better frequency precision but poor temporal and vice versa but depends on:
- analysis goals
- short bursts of oscillations
- narrow frequency range = larger number of cycles
- specific latency = fewer cycles
What are some TRF issues?
difficult to visualise or make quantative comparisons of power across frequency bands
Difficult to aggregate across participants
Difficult to differentiate task related activity from background activity
Difficult to meet the normality assumption (raw power is positively skewed)
What is event-related (de)synchronisation?
Changes in spectral power in respect of baseline
Decrease of band power = ERD
increase of band power = ERS
What is total oscillations equal of?
evoked oscillations + induced oscillations
How to choose TFR baseline?
Baseline may be -500ms to -200ms or -400ms to -100 ms
try not to include 0 in the baseline
Use pretrial period as baseline
use conditions average baseline
Data of the whole trial can be used as a baseline
Real oscillations or not?
TRD (Fourior transform) is a mathematical abstract and not a proof of physical existence of oscillations
show wider frequency range
If an effect is mainly localised within a smaller range than more convincing evidence
Show frequencies above and below the effect
