Efficient Sensing for Compressive Estimation of Frequency of a Real Sinusoid

Linear least squares (LS) frequency estimators are popular because they are closed-form and easy to implement. However, they are applicable to compressive frequency estimation only after reconstruction. This is because compressive sensing (CS) breaks up the temporal order of the original sinusoidal samples. This correspondence proposes an efficient sensing scheme to obtain CS samples. They are sums of the Nyquist-rate samples of the signal. There is no need for matrix multiplications nor the Random-Modulator-Preintegrator. A modified LS estimator is able to estimate frequency directly from the CS samples, without reconstruction. This estimator has accuracy that matches the theoretical lower bound, as shown by two examples.