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Signal processing can be performed in time domain as well as intransform domain. Frequency domain is perhaps the most widely used domain for transform domain signal processing. In this paper we analyze sequency domain (SD) signal processing as an alternate to the conventional frequency domain signal processing. We perform signal processing in sequency domain using conjugate-symmetric sequencyordered complex Hadamard transform and compare the results with those of discrete Fourier transform. We observe that in comparison with frequency spectrum, spectral energy of sequency spectrum is spread over the entire spectrum. We performed signal and image denoising in SD and found that our designed SD filters effectively denoise the signals.

Spatiochromatic information of colour images is analysed in sequency domain using CIE La*b* colour space. RGB image is processed in transform domain using spatiochromatic-conjugate symmetric sequency ordered complex Hadamard transform (SC-CS-SCHT). Spatiochromatic vectors (a*, b* and a*b*) are considered as real, imaginary and complex inputs to the SC-CS-SCHT. This transform has symmetry properties that are similar to the discrete Fourier transform. Resultant phasor paths are observed with respect to different input signals along the unit complex plane. In sequency domain opponent colour paths are discussed and applied on two-dimensional signals. Peak signal-to-noise ratio is measured for ideal lowpass filter.

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This Letter presents the quaternion conjugate symmetric-sequency ordered complex Hadamard transform (QCS-SCHT). The purpose of this research is to present the idea of the quaternion in sequency domain that is based on four complexified terms including real and imaginary values are discussed and developed with different types of quaternions planes for QCS-SCHT. QCS-SCHT is discussed for colour image processing.