Method for applying a discrete fourier transform, dft, to a sequence of samples of a sensor signal, processor circuit for performing the method, radar sensor and motor vehicle

A processor circuit for applying a P-dimensional discrete Fourier transform (“DFT”) to a sequence of N samples of a sensor signal, with P, N>2, and configured to:

• receive one of the samples at a time;
• and
• perform the following in response to receiving a new one of the samples or a group of consecutive new samples, comprising a predefined number J of samples, with 1<J<N
• provide, for each new sample xn, an order index n indicating which one of the 1 to N samples has been received, wherein n in 1, . . . , N,
• prove, for each new sample, a corresponding DFT vector {right arrow over (d)}(n), wherein the DFT vector {right arrow over (d)}(n) is selected or generated depending on the order index n of the sample, wherein the DFT vector {right arrow over (d)}(n) comprises P phasor values that are derived from frequency points fp of the P-dimensional DFT by S*exp(−i 2 π fp tn) with p in 1, . . . , P the index of the phasor value in the DFT vector {right arrow over (d)}(n) and S a scaling factor and tn the sampling time of the new sample xn and i the imaginary unit with i2=−1;
• apply the respective new sample xn as a multiplication factor to its corresponding DFT vector {right arrow over (d)}(n) for generating a respective spectral contribution vector Δ{right arrow over (y)}(n)={right arrow over (d)}(n)xn;
• and
• add the respective spectral contribution vector Δ{right arrow over (y)}(n) to an accumulation vector {right arrow over (y)}(n)=Δ{right arrow over (y)}(n)+{right arrow over (y)}(n-1),
• when for all N samples their corresponding resulting contribution vector has been added to the accumulation vector, provide the accumulation vector {right arrow over (y)}(N) as DFT spectral coefficients of the N samples.

A RADAR device, comprising:

• a sensor for generating a sensor signal;
• and
• a processor circuit for applying a P-dimensional discrete Fourier transform (“DFT”) to a sequence of N samples of the sensor signal, with P, N>2, and configured to
• receive one of the samples at a time, and
• perform the following in response to receiving a new one of the samples or a group of consecutive new samples, comprising a predefined number J of samples, with 1<J<N
• provide, for each new sample xn, an order index n indicating which one of the 1 to N samples has been received, wherein n in 1, . . . , N,
• prove, for each new sample, a corresponding DFT vector {right arrow over (d)}(n), wherein the DFT vector {right arrow over (d)}(n) is selected or generated depending on the order index n of the sample, wherein the DFT vector {right arrow over (d)}(n) comprises P phasor values that are derived from frequency points fp of the P-dimensional DFT by S*exp(−i 2 π fp tn) with p in 1, . . . , P the index of the phasor value in the DFT vector {right arrow over (d)}(n) and S a scaling factor and tn the sampling time of the new sample xn and i the imaginary unit with i2=−1;
• apply the respective new sample xn as a multiplication factor to its corresponding DFT vector {right arrow over (d)}(n) for generating a respective spectral contribution vector Δ{right arrow over (y)}(n)={right arrow over (d)}(n) xn;
• and
• add the respective spectral contribution vector Δ{right arrow over (y)}(n) to an accumulation vector {right arrow over (y)}(n)=Δ{right arrow over (y)}(n)+{right arrow over (y)}(n-1),
• when for all N samples their corresponding resulting contribution vector has been added to the accumulation vector, provide the accumulation vector {right arrow over (y)}(N) as DFT spectral coefficients of the N samples.