ECG compression using discrete cosine transform (DCT).

The input signal is record 100 from the Physionet MIT-BIH Arrhythmia database. The signal is a 2-minute segment of ECG sampled at 360 Hz. When loaded into MATLAB, each sample is represented by a 8-byte double. Thus, the total size of the input signal is (120 sec) * (360 samples/sec) * (8 bytes) = 345600 bytes. Prior to compression, the signal is scaled (subtract by mean, divided by standard deviation).

Configurable compression parameters:

1. ENERGY_THRESH: Fraction of the energy of the DCT coefficients used to determine a threshold value. Default = 0.90.
2. QUANT_PRECISION: Number of bits to quantize remaining DCT coefficients to. Default = 8.

1. Calculate DCT coefficients using MATLAB's dct function.

2. Determine the threshold on the DCT coefficients as the value corresponding to ENERGY_THRESH% of the cumulative sum.

3. Save index of all coefficients less than the threshold - these are the coefficients to be set to 0 during decompression.

4. Quantize the remaining coefficients by mapping the distribution to a range of signed int defined by QUANT_PRECISION. For 8-bit precision, the distribution would be mapped to 256 bins over the values [-128,127].

5. The output from the compression function are:

   • b0: original DCT coefficients
   • b_quant: quantized DCT coefficients with zeros removed
   • b_limits: limits of the distribution of original coefficients
   • zeroIdx: binary array where 1 represents the position of a zero

   Thus, the size of the compressed signal is defined as the total number of bytes in b_quant, b_limits, and zeroIdx.

1. Map quantized coefficients (b) back to original distribution defined by QUANT_PRECISION and b_lim. The coefficients defined in zeroIdx are set to zero.
2. Reconstruct the signal using MATLAB's idct function.

Percent root mean square difference (PRD) is an accuracy metric defined as the square root of the mean square error divided to the total energy ratio.