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+# Doppler correction
+This is a brief description of how Doppler correction is implemented in the FIR_Filter and subsequent DelayAndBandpass correction.
+
+
+Let the intrinsic sky signal be *g(t)* with its Fourier transform *G(f)*. Due to the Doppler shift, the measured signal will have a frequency shift *f_0* and in order to get back the orignal signal, we shift the measured signal Fourier transform as *G(f-f_0)*, which is done in continuous time by multiplication of *g(t)* with *exp(-j 2 pi f_0 t)*.
+
+<img src="phaseramp.png" width="900"/>
+
+The signal streaming to FIR_Filter is a discrete time signal, about 190k samples per one block of about 1 second duration (see the figure). The sampling frequency is *f_s* = clock frequency/1024.
+The delays at the start of the block of data and after the end of the block are *tau0* and *tau1*, respectively.
+
+Let *t* denote time within the block and *T* be the duration of the block, so *t* in *[0,T]*.
+The linear delay for the sample at time *t* is *tau=tau1 (t/T) + tau0(1-t/T)*. The corresponding discrete time exponential is *exp(-j 2 pi f tau)*. Discarding the constant terms (that do not vary with time), the exponential becomes  *exp(-j 2 pi f (tau1-tau0)/T t)*. The subband frequency is *f*.
+
+As seen in the figure, each block is divided to many FFT blocks, so within each block, we use the same delay gradient *(tau0-tau0)/T* to calculate the phase ramp. In other words, the constant part of the delay ramp is not used as it will only increase decorelation, not affecting the needed shift in frequency.
+
+To summarize, the exact term used at channel *chan* is *j 2 pi (f/f_s) (tau1-tau0)/NR_FFT_BLOCKS chan/NR_CHANNELS*. 
+
+Due to this correction, the shift in channels is *(tau1-tau0)/NR_FFT_BLOCKS (f/f_s)*. The corresponding shift in frequency is *(tau1-tau0)/NR_FFT_BLOCKS (f/NR_CHANNELS)*.
+
+The Doppler correction is not affected by the rotation of the dipoles, so both polarizations get the same correction (unless the delays for each polarization is different).
+The bandpass correction is modified by linear interpolation of the bandpass correction weights with the appropriate channel shift.
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