Abstract—Speech recognition is still a growing field of importance. The growth in computing power will open its strong potentials for full use in the near future. Spectrum analysis is an elementary operation in speech recognition. Fast Fourier Transform (FFT) has been a traditional technique to analyze frequency spectrum of the signals in speech recognition. FFT is computationally complex especially with imaginary numbers. The Discrete Tchebichef Transform (DTT) is proposed instead of the popular FFT. DTT has lower computational complexity and it does not require complex transform dealing with imaginary numbers. This paper proposes a novel approach based on 256 discrete orthonormal Tchebichef polynomials as efficient technique to analyze a vowel and a consonant in spectral frequency of speech recognition. The comparison between 1024 discrete orthonormal Tchebichef transform and 256 discrete orthonormal Tchebichef transform has been done. The preliminary experimental results show that 256 DTT has the potential to be more efficient to transform time domain into frequency domain for speech recognition. 256 DTT produces simpler output than 1024 DTT in frequency spectrum. At the same time, 256 Discrete Tchebichef Transform can produce concurrently four formants F 1 , F 2 , F 3 and F 4 . Index Terms—Speech recognition, spectrum analysis, Fast Fourier Transforms and Discrete Tchebichef Transform. I. INTRODUCTION Spectrum analysis method using Fourier transform is widely used for digital signal processing applicable for spectrum analysis of speech recognition. Speech recognition requires heavy processing on large sample windowed data. Typically, each window consumes 1024 sample data. Since the window is large, an efficient FFT has been employed to speed up the process. 1024 sample data FFT computation is considered the main basic algorithm for several digital signals processing [1]. FFT is a traditional technique to analyze frequency spectrum of speech recognition. The FFT is often used to compute numerical approximations to continuous Fourier. However, a straightforward application of the FFT often requires a large FFT to be performed even though most of the input data may be zero [2]. FFT is a complex transform which requires operating on imaginary Manuscript received March 22, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Mohamed Othman. Ferda Ernawan is with the Faculty of Information and Communication Technology, Universitas Dian Nuswantoro (UDINUS), Semarang, Indonesia (e-mail: ferda1902@gmail.com ). Nur Azman Abu is with the Faculty of Information and Communication Technology, Universiti Teknikal Malaysia Melaka (UTeM), Melaka, Malaysia (e-mail: nura@utem.edu.my ). numbers. It is a complex exponential function that defines a complex sinusoid for a given frequency. The Discrete Tchebichef Transform (DTT) is another transform method based on discrete Tchebichef polynomials [3][4]. This paper proposes an approach based on 256 discrete orthonormal Tchebichef polynomials to analyze spectral frequency for speech recognition. DTT is used to avoid the complex computation of FFT. DTT has a potential next candidate to transform time domain into frequency domain in speech recognition. DTT has a lower computational complexity and it does not require complex transform unlike continuous orthonormal transforms [5]. DTT does not involve any numerical approximation on friendly domain. The Tchebichef polynomials have unit weight and algebraic recurrence relations involving real coefficients. These factors in effect make DTT suitable for transforming the signal from time domain into frequency domain for speech recognition. DTT has been applied in several computer vision and image processing application in previous work. For examples, DTT is used in image analysis [6], texture segmentation [7], image watermarking [8], image reconstruction [3][9], image compression [10] and spectrum analysis of speech recognition [5][11]. The organization of the paper is as follows. The next section gives a brief description on FFT and DTT. The matrix implementation of orthonormal tchebichef polynomials are presented in section III. Section IV shows the experiment results of speech signal coefficient of Discrete Tchebichef Transform, spectrum analysis, frequency formants and time taken performance. Section V presents the comparison of spectrum analysis, frequency formants and time taken performance between 1024 DTT and 256 DTT. Finally, section VI concludes the comparison of spectrum analysis using 1024 DTT and 256 DTT in terms of speech recognition. II. TRANSFORMATION DOMAIN FFT is an efficient algorithm that can perform Discrete Fourier Transform (DFT). FFT is applied in order to convert time domain signals ݔ() into the frequency domain () . Let the sequence of  complex numbers ݔ ଴ ݔ,…, ேଵ represent a given time domain windowed signal. The following equation defines the Fast Fourier Transform of ݔ(): () = ෍ ݔ() ଶగ௜ ே (௝ଵ)(௞ଵ) ே ௝ୀଵ (1) Efficient Discrete Tchebichef on Spectrum Analysis of Speech Recognition Ferda Ernawan and Nur Azman Abu International Journal of Machine Learning and Computing, Vol.1, No. 1, April 2011 1