Program Type
Honors
Faculty Advisor
Dr. Xinli Xiao
Document Type
Poster
Location
Face-to-face
Start Date
25-4-2023 9:00 AM
Recommended Citation
McKinley, Dillon C., "Analysis of the Discrete Cosine Transform Coefficients" (2023). ATU Research Symposium. 44.
https://orc.library.atu.edu/atu_rs/2023/2023/44
Included in
Apr 25th, 9:00 AM
Analysis of the Discrete Cosine Transform Coefficients
Face-to-face
Comments
In this report, the driving goal was to discover the relationship of the discrete cosine transform (DCT) coefficients to the original signal being tested through the correlations between amplitude and frequency within the frequency domain. Due to the complex nature of DCT’s, the coding language Python was used to calculate the large matrices required to process signals into the frequency domain and generate graphs to represent them. To find the relationships between the DCT coefficients and the original signal, various manipulations were performed on the initial information. First, it was tested how varying the amount of samples taken for the discrete analysis of the signal would affect the coefficients being outputted. Then, taking the signal at different intervals was tested. Altering the lengths of the intervals would affect the period of the periodic extensions of the signal in which the DCT analyzes. Once the DCT is performed on the signal, the values of the amplitude at given frequencies are the coefficients used in the discrete cosine series that is used to reconstruct the original signal. It was found that altering the number of samples to a certain extend would limit the information that was required for reconstruction. Changing the interval taken from the original signal would change frequency where key amplitude for reconstruction would appear. It was also found that at certain intervals, the graph would spike on values that were not whole numbers which the DCT could not directly take a sample of, making the graph more erratic to compensate.