Spectrograms in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the spectrogram of signal x using window length 256.

MATLAB

spectrogram(x, [1], 128, 256, fs);

Drag options to blanks, or click blank then click option'

A256

B512

C128

D64

Attempts:

3 left

💡 Hint

Common Mistakes

Using the overlap length instead of window length.

Confusing window length with FFT length.

The window length parameter defines the size of each segment. Using 256 matches the desired window length.

2fill in blank

medium

Complete the code to set the overlap between segments to 75% of the window length.

MATLAB

window_length = 256;
overlap = [1];
spectrogram(x, window_length, overlap, 512, fs);

Drag options to blanks, or click blank then click option'

A128

B64

C192

D256

Attempts:

3 left

💡 Hint

Common Mistakes

Using 128 which is 50% overlap.

Using the full window length as overlap.

75% of 256 is 192, so the overlap should be set to 192 samples.

3fill in blank

hard

Fix the error in the code to compute the spectrogram with a Hamming window.

MATLAB

window = [1](256);
spectrogram(x, window, 128, 512, fs);

Drag options to blanks, or click blank then click option'

Ahanning

Brectwin

Cblackman

Dhamming

Attempts:

3 left

💡 Hint

Common Mistakes

Using hanning instead of hamming.

Using a rectangular window by mistake.

The Hamming window is created by the function hamming in MATLAB.

4fill in blank

hard

Fill both blanks to create a spectrogram with a Blackman window and 50% overlap.

MATLAB

window = [1](512);
overlap = [2];
spectrogram(x, window, overlap, 1024, fs);

Drag options to blanks, or click blank then click option'

Ablackman

B256

C128

Dhamming

Attempts:

3 left

💡 Hint

Common Mistakes

Using hamming instead of blackman.

Using 128 instead of 256 for overlap.

Blackman window is created by blackman(512). 50% overlap of 512 is 256.

5fill in blank

hard

Fill all three blanks to compute a spectrogram with a Hanning window, 75% overlap, and FFT length 1024.

MATLAB

window = [1](1024);
overlap = [2];
fft_length = [3];
spectrogram(x, window, overlap, fft_length, fs);

Drag options to blanks, or click blank then click option'

Ahanning

B768

C1024

Dblackman

Attempts:

3 left

💡 Hint

Common Mistakes

Using blackman instead of hanning.

Using 512 instead of 768 for overlap.

Using wrong FFT length.

Hanning window is created by hanning(1024). 75% overlap of 1024 is 768. FFT length is 1024.

Practice

1. What does a spectrogram primarily display in signal processing?

easy

A. The total energy of a signal

B. How frequencies change over time in a signal

C. The amplitude of a signal at a single point

D. The phase shift of a signal

Solution

1. Step 1: Understand the purpose of a spectrogram

   A spectrogram is a visual tool that shows how the frequency content of a signal varies over time.

2. Step 2: Compare options with the definition

   Only How frequencies change over time in a signal correctly describes this as frequency changes over time, while others describe different signal properties.

3. Final Answer:

   How frequencies change over time in a signal -> Option B

4. Quick Check:

   Spectrogram = frequency vs time [OK]

Hint: Spectrogram = frequency changes over time [OK]

Common Mistakes:

• Confusing amplitude with frequency
• Thinking spectrogram shows total energy
• Mixing phase shift with frequency content

2. Which of the following is the correct syntax to create a spectrogram in MATLAB for signal x with window size 256 and overlap 128?

easy

A. spectrogram(x,256,128)

B. spectrogram(x,128,256)

C. spectrogram(256,x,128)

D. spectrogram(x,128)

Solution

1. Step 1: Recall MATLAB spectrogram syntax

   The syntax is spectrogram(signal,window,overlap), so the window size comes before overlap.

2. Step 2: Match parameters to syntax

   spectrogram(x,256,128) correctly uses spectrogram(x,256,128) where 256 is window size and 128 is overlap.

3. Final Answer:

   spectrogram(x,256,128) -> Option A

4. Quick Check:

   Correct order: signal, window, overlap [OK]

Hint: Remember: spectrogram(signal, window, overlap) [OK]

Common Mistakes:

• Swapping window and overlap values
• Passing window size as first argument
• Omitting required parameters

3. What will be the output size of the matrix S when running [S,F,T] = spectrogram(x,128,64,256,1000); if x is a 1-second signal sampled at 1000 Hz?

medium

A. 256 rows by 15 columns

B. 128 rows by 16 columns

C. 129 rows by 14 columns

D. 129 rows by 16 columns

Solution

1. Step 1: Calculate frequency bins (rows)

   Frequency bins = nfft/2 + 1 = 256/2 + 1 = 129 rows.

2. Step 2: Calculate time bins (columns)

   Signal length = 1000 samples, window=128, overlap=64, step = 128-64=64 samples.
   Number of segments = floor((1000-128)/64) + 1 = floor(872/64) + 1 = 13 + 1 = 14 columns.

3. Final Answer:

   129 rows by 14 columns -> Option C

4. Quick Check:

   Rows = 129, Columns = 14 [OK]

Hint: Rows = nfft/2+1, columns depend on window and overlap [OK]

Common Mistakes:

• Confusing nfft with window size for rows
• Miscounting number of segments
• Ignoring overlap in time bins calculation

4. Given the code snippet:

x = randn(1,1000);
[S,F,T] = spectrogram(x,256,128,512,1000);
imagesc(T,F,abs(S)); axis xy;

The spectrogram plot looks very blurry. What is the most likely cause?

medium

A. Sampling frequency is too low

B. Overlap is too small, causing gaps in data

C. nfft is smaller than window size, causing error

D. Window size is too large, causing poor time resolution

Solution

1. Step 1: Analyze window size effect on resolution

   A large window size (256) smooths over time, reducing time resolution and causing blur.

2. Step 2: Check other parameters

   Overlap is 128 (50%), which is typical and not causing gaps.
   nfft (512) is larger than window (256), which is valid.
   Sampling frequency (1000) is standard.

3. Final Answer:

   Window size is too large, causing poor time resolution -> Option D

4. Quick Check:

   Large window = poor time resolution [OK]

Hint: Large window = better frequency, worse time resolution [OK]

Common Mistakes:

• Confusing overlap with window size effect
• Assuming nfft smaller than window causes blur
• Blaming sampling frequency for blur

5. You want to analyze a signal with rapidly changing frequencies using MATLAB's spectrogram. Which combination of parameters will best capture quick changes without losing frequency detail?

hard

A. Small window size, large overlap, moderate nfft

B. Large window size, large overlap, small nfft

C. Large window size, small overlap, large nfft

D. Small window size, small overlap, large nfft

Solution

1. Step 1: Understand trade-offs in spectrogram parameters

   Small window size improves time resolution to capture rapid changes.
   Large overlap ensures smooth transitions between windows.
   Moderate nfft balances frequency resolution without excessive computation.

2. Step 2: Evaluate options

   Small window size, large overlap, moderate nfft matches these criteria.
   Small window size, small overlap, large nfft has small overlap, causing gaps.
   Options B and C use large windows, reducing time resolution.

3. Final Answer:

   Small window size, large overlap, moderate nfft -> Option A

4. Quick Check:

   Quick changes need small window + large overlap [OK]

Hint: Small window + large overlap = best for fast changes [OK]

Common Mistakes:

• Using large window for fast changes
• Ignoring overlap size
• Choosing too small nfft losing frequency detail