Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

A nonstationary signal is a signal whose frequency content changes
with time. The *spectrogram* of a nonstationary
signal is an estimate of the time evolution of its frequency content.
To construct the spectrogram of a nonstationary signal, **Signal Analyzer** follows these
steps:

Divide the signal into equal-length segments. The segments must be short enough that the frequency content of the signal does not change appreciably within a segment. The segments may or may not overlap.

Window each segment and compute its spectrum to get the

*short-time Fourier transform*.Display segment-by-segment the power of each spectrum in decibels. Depict the magnitudes side-by-side as an image with magnitude-dependent colormap.

The spectrogram view is available in displays that contain only one signal.

To construct a spectrogram, first divide the signal into possibly
overlapping segments. In **Signal
Analyzer**, you can control the length of the segments and the
amount of overlap between adjoining segments using **Time
Resolution** and **Overlap**. If you do
not specify the length and overlap, **Signal Analyzer** chooses
a length based on the entire length of the signal, and 50% overlap.
The app aligns the time axis of the spectrogram with the axis of the
time-domain plot.

On the **Spectrogram** tab, in the **Time
Resolution** section, click **Specify**.

If the signal does not have time information, specify the time resolution (segment length) in samples. The time resolution must be an integer greater than or equal to 1 and smaller than or equal to the signal length.

If the signal has time information, specify the time resolution in seconds. The app converts the result into a number of samples and rounds it to the nearest integer that is less than or equal to the number but not smaller than 1. The time resolution must be smaller than or equal to the signal duration.

Specify the overlap as a percentage of the segment length. The app converts the result into a number of samples and rounds it to the nearest integer that is less than or equal to the number.

If you select **Auto** for the time resolution computation, then
**Signal Analyzer** uses the length of the entire signal to choose the
length of the segments. The app sets the time resolution as

$$\lceil \frac{N}{d}\rceil $$

Signal Length (N) | Divisor (d) | Segment Length |
---|---|---|

`2` samples – `63`
samples | `2` | `1` sample – `32`
samples |

`64` samples – `255`
samples | `8` | `8` samples – `32`
samples |

`256` samples – `2047`
samples | `8` | `32` samples – `256`
samples |

`2048` samples – `4095`
samples | `16` | `128` samples – `256`
samples |

`4096` samples – `8191`
samples | `32` | `128` samples – `256`
samples |

`8192` samples – `16383`
samples | `64` | `128` samples – `256`
samples |

`16384` samples – N
samples | `128` | `128` samples – ⌈N /
`128` ⌉ samples |

You can still specify the overlap between adjoining segments. Specifying the overlap changes the number of segments. Segments that extend beyond the signal endpoint are zero-padded.

Consider the seven-sample signal ```
[s0 s1 s2 s3 s4 s5
s6]
```

. Because ⌈7/2⌉ = ⌈3.5⌉ = 4, the app divides the signal into
two segments of length four when there is no overlap. The number of
segments changes as the overlap increases.

Number of Overlapping Samples | Resulting Segments |
---|---|

`0` | s0 s1 s2 s3 s4 s5 s6 0 |

`1` | s0 s1 s2 s3 s3 s4 s5 s6 |

`2` | s0 s1 s2 s3 s2 s3 s4 s5 s4 s5 s6 0 |

`3` | s0 s1 s2 s3 s1 s2 s3 s4 s2 s3 s4 s5 s3 s4 s5 s6 |

Once the segment length and overlap are set, the number of segments and their edge locations stay fixed and are independent of any zooming or panning. When you zoom and pan, the app computes and displays the spectrogram using the segments that fall within the visible zoomed-in region of interest.

The app:

Aligns the time axis of the spectrogram with the axis of the corresponding time-domain plot. That way, the spectral content at a given time aligns with its occurrence.

For nonzero overlap, extends the first and last segments to the signal endpoints.

Zero-pads the signal if the last segment extends beyond the signal endpoint.

When the segments have 0% overlap, each segment is centered at the actual time of occurrence. When the overlap is nonzero, the alignment of the spectrogram time axis with the time-domain axis has the effect that the first and last time intervals are elongated. All other time intervals are of the same length. In other words, the center of each segment, except for the first and last, corresponds to the actual time of occurrence. Consider this example:

After **Signal Analyzer** divides the signal into overlapping segments, the app windows
each segment with a Kaiser window. The shape factor *β* of the window,
and therefore the *leakage*, is adjustable.

The leakage used to compute the signal spectrum and the leakage used to window the spectrogram segments are independent of each other. You can adjust them separately.

The app then computes the spectrum of each segment, using the procedure outlined
in Spectrum Computation in Signal Analyzer. In
summary, **Signal Analyzer** finds a compromise between the spectral resolution
achievable with the entire length of the segment and the performance limitations that
result from computing large FFTs.

If the resolution resulting from analyzing the full segment is achievable, the app computes a single modified periodogram of the whole segment using a Kaiser window with the specified shape factor.

If the resolution resulting from analyzing the full segment is not achievable, the app computes a Welch periodogram: It divides the segment into overlapping subsegments, windows each subsegment, and averages the periodograms of the subsegments. The app chooses the subsegment size, the window, and the overlap so that the composite periodogram is equivalent to a modified periodogram of the whole segment with the specified Kaiser window.

The app displays the power of the short-time Fourier transform
in decibels, using a color bar with the default MATLAB^{®} colormap.
The color bar comprises the full power range of the spectrogram and
does not change if you zoom or pan.

You can change the magnitude levels represented by a given color
range. On the **Spectrogram** tab, change the minimum
and maximum power values to display. You can also set the colormap
so that it comprises the full power range of the zoomed-in section
of the spectrogram. On the **Display** tab, click
the scale color button .

- Find Delay Between Correlated Signals
- Plot Signals from the Command Line
- Resolve Tones by Varying Window Leakage
- Analyze Signals with Inherent Time Information
- Spectrogram View of Dial Tone Signal
- Find Interference Using Persistence Spectrum
- Extract Regions of Interest from Whale Song
- Find and Track Ridges Using Reassigned Spectrogram

Was this topic helpful?