EE313 Linear Systems & Signals - Mini-Project #1 Hints - Fall 2024

• Scope and format are described at the bottom of the homework hints page.
• Demos. Here are demos of the Shepard Scale effect with a connection to Escher's drawing "Ascending and Descending’" mentioned in the lab assignment. The demos are by U. Baysan and F. Macpherson at the University of Glasgow (July 2017).
• Article. The link in the lab assignment to an article by the Acoustical Society of America on the Shepard Scale effect is broken. Here is a recent article: "Timbral Shepard-illusion reveals ambiguity and context sensitivity of brightness perception", The Journal of the Acoustical Society of America, vol. 143, no. 2, Feb. 6, 2018.
• Middle A on the Western scale. In the DSP First lab assignment, the key numbers (shaded) in the piano are different from those in the Musical Instrument Digital Interface (MIDI) standard. For example, the key number for A4 is 49 according to the lab assignment; however, according to MIDI uses 69. Please use 49 for the key number in your solution.
• Audio playback. Be sure to create one vector for your entire audio signal. A way to concatenate row vectors into a single vector is

      audiovector = [ Cnotes pauseVec Dnotes pauseVec Enotes pauseVec ... ];
  

  Since several sinusoidal signals are being added together, the amplitude range of audiovector will exceed the range of -1 to 1, and hence, using the sound command will result in clipping. For playback, you could either
  • use the soundsc command, OR
  • scale the audio signal to be between -1 and 1 in amplitude

        audiovector = audiovector - mean(audiovector);
        audiovector = audiovector / (max(abs(audiovector));
    

    and then play the vector using the sound command.

  If you were use the sound command for each note and the pause command for each pause, the timing will be off because you'll be experiencing variable delays from the operating system to send data to the playback subsystem and for the playback subsystem to complete the playback on the vector of samples, and variable delays in implementing the pause duration.

  You can also save the scaled vector to a wave file using the command

      audiowrite(filename, audiovector, fs);
  

  and play it back as a file on your laptop independent of Matlab. The wave format is desirable because it does not apply any compression to the signal.

  The audiowrite command will clip amplitude values outside the range of -1 and 1.

• Sigma Please use sigma = 1 in Section 3 and sigma = 2 for Section 4.
• Spectrogram. The frequency resolution is f_s / N where f_s is the sampling rate and N is the number of samples in each segment / block. For example, for f_s = 22050 Hz and N = 256, the frequency resolution would be 86 Hz. Hence, frequencies in the audio signal below 86 Hz cannot be separated in the spectrogram. Be sure to choose N to be able to separate the frequenices present in the audio signal.
• Matlab code
  • key2note.m. Generates a sinusoidal signal at a given frequency for a specified time interval. The frequency is indicated by a piano key number, where 49 means note A at 440 Hz.
  • FrequencyWeighting.m. Generates a scalar value corresponding to a Gaussian weight for a given frequency relative to a reference frequency.
  • tuneup3fall2024.m. Solution for parts 2 and 3.1 for the Shepard Scale mini-project.

bevans@ece.utexas.edu