9 Assessing Spectrograms

Question 1

What is a spectrogram?

Answer 1

The spectrogram is defined as the display of successive spectra
calculated from time intervals T_i = L Δt which are shorter than
the total time of the recordings T = N Δt such that T_i < T, L < N

Question 2

The time interval T_i ?

Answer 2

• The time interval Ti used for the calculation of the spectrum is defined by a moving window.
• A moving window is defined by a fixed length window with a start time which increases for each calculation of a spectrum
• This increase is named time shift of the spectrogram and it is typically some fraction of the time interval T_i

Question 3

The choice of window and time shift?

Answer 3

The choice for the window and the time shift used for the calculation of the spectrogram depends on the application

Question 4

A typical spectrogram with a rectangular window of length Ti uses
a time shift of T_i , before shift:

Answer 4

Question 5

A typical spectrogram with a rectangular window of length Ti uses
a time shift of T_i , after shift:

Answer 5

Question 6

A typical spectrogram with a Hannning window of length Ti uses
a time shift of T_i/2 before shift

Answer 6

Question 7

A typical spectrogram with a Hannning window of length Ti uses
a time shift of T_i/2 after shift

Answer 7

Question 8

The equation for the spectrogram spectral coefficients?

Answer 8

Question 9

The uncertainty principle?

Answer 9

The uncertainty principle for the spectrogram states that the product of the time resolution Ti and the frequency resolution Δf is constant:

T_iΔf = 1

Question 10

Proof of the uncertainty principle?

Answer 10

Question 11

What does a spectrogram display?

Answer 11

The spectrogram displays the temporal evolution of the spectral content of a signal

Question 12

Dimensions of a spectrogram?

Answer 12

time and frequency

Question 13

how are amplitudes displayed on a spectrogram?

Answer 13

• As a result, the spectral amplitudes are displayed in a third dimension, typically as a colour coded image or gray scale image
• On colour coded spectrograms, small spectral amplitudes are typically displayed in blue and large spectral amplitudes in red
• In gray scale coded spectrograms, small spectral amplitudes are typically displayed in black and large spectral amplitudes in white

Question 14

The two fundamentally different pieces of information displayed by a spectrogram?

Answer 14

• signals which are localised in a narrow range of frequencies,
  e. g., a whistle, or a radio carrier wave
• signals which localised in a short time frame, e.g., a hand

clap, or a radio pulse

Question 15

Uses of spectrogram?

Answer 15

The spectrogram is typically used to detect signals and to determine their time/frequency (or spectral) evolution

Question 16

spectrogram successful detection?

Answer 16

For the successful detection of signals in the spectrogram, it is critically important to determine the necessary frequency resolution and the minimum length of the time interval T_i

Question 17

Spectrogram and leakage?

Answer 17

• In addition, the possibility for leakage needs to be considered
• Choosing the wrong frequency resolution can mask the signal of interest and result in wrong conclusions

Question 18

spectrogram, low sample rate

Answer 18

Question 19

spectrogram, high sample rate

Answer 19