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Stroke, which is seen nowadays frequently, is the rapidly developing loss of brain functions due to a disturbance in the blood vessels supplying blood to the brain. The main reason for the stroke is the emboli which are particles bigger than red blood cells. Emboli can be detected by Doppler ultrasound. Embolic Doppler ultrasound signals are short duration transient like signals. These signals can be obtained from in-phase and quadrature-phase parts of the quadrature Doppler signals as forward and reverse signals by using the phase relationship between in-phase and quadrature-phase signals. Discrete wavelet transform is one of the methods used for analyzing these signals. A desired property in discrete wavelet transform is phase shift-invariance which can not be provided by ordinary discrete wavelet transform. To overcome this disadvantage dual-tree complex wavelet transform was introduced. But Doppler signals are dual channel signals and dual-tree complex wavelet transform must be applied twice. Therefore complexity of the transform increases. In this work, a new transform method reducing computational complexity is introduced.