Performance Parameter Based Comparison of Various Transforms

Abstract

In this paper we present analysis and implementation of Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) with “Symlet 4 (Sym 4)” and “Biorthogonal 3.5 (Bior 3.5)” and Slantlet Transform. The DCT transforms signal and images from spatial domain to frequency domain. The DWT separates 1-D signal into approximate and detail information and 2-D signal into four sub-bands LL, LH, HL, and HH. The Slantlet Transform is known as orthogonal discrete wavelet transform. It separates 1-D signal into two sub-bands approximate and detail information and 2-D signal into four sub-bands LL, LH, HL, and HH respectively. In this paper we present decomposition and reconstruction of 1-D signal (ECG) and 2-D signal(image) by using DCT, DWT with “sym 4” and “Bior 3.5” and Slantlet Transform. Signal decomposition and reconstruction is important tool for compression, watermarking and steganography applications. The amount of distortion between input signal and reconstructed signal and the quality of reconstructed signal is evaluated by calculating statistical parameters. The quality of reconstructed signal by using DCT, DWT and Slantlet Transform is measured by calculating statistical parameters such as Mean Squared Error (MSE), Peak Signal to Noise Ratio (PSNR) and Normalised Root Mean Squared Error (NRMSE) to analyse performance of all these transforms respectively. Our experimental results have shown that MSE using DCT and Bior 3.5 is less than MSE using Slantlet transform and Sym 4 respectively. Hence DCT and DWT with Bior 3.5 proves better for signal decomposition and reconstruction than DWT with Sym 4 and Slantlet Transform.