{-| Filter design and plotting of frequency responses. -} module SDR.FilterDesign ( -- * Sinc Function sinc, -- * Root raised cosine srrc, -- * Windows hanning, hamming, blackman, -- * Convenience Functions windowedSinc, -- * Frequency Response Plot plotFrequency ) where import Graphics.Rendering.Chart.Easy import Graphics.Rendering.Chart.Backend.Cairo import Data.Complex import qualified Data.Vector.Generic as VG -- | Compute a sinc function sinc :: (Floating n, VG.Vector v n) => Int -- ^ The length. Must be odd. -> n -- ^ The cutoff frequency (from 0 to 1) -> v n sinc size cutoff = VG.generate size (func . (-) ((size - 1) `quot` 2)) where func 0 = cutoff func idx = sin (pi * cutoff * fromIntegral idx) / (fromIntegral idx * pi) -- | Compute a Hanning window. hanning :: (Floating n, VG.Vector v n) => Int -- ^ The length of the window -> v n hanning size = VG.generate size func where func idx = 0.5 * (1 - cos((2 * pi * fromIntegral idx) / (fromIntegral size - 1))) -- | Compute a Hamming window. hamming :: (Floating n, VG.Vector v n) => Int -- ^ The length of the window -> v n hamming size = VG.generate size func where func idx = 0.54 - 0.46 * cos((2 * pi * fromIntegral idx) / (fromIntegral size - 1)) -- | Compute a Blackman window. blackman :: (Floating n, VG.Vector v n) => Int -- ^ The length of the window -> v n blackman size = VG.generate size func where func idx = 0.42 - 0.5 * cos((2 * pi * fromIntegral idx) / (fromIntegral size - 1)) + 0.08 * cos((4 * pi * fromIntegral idx) / (fromIntegral size - 1)) windowedSinc :: (Floating n, VG.Vector v n) => Int -- ^ The length -> n -- ^ The cutoff frequency (from 0 to 1) -> (Int -> v n) -- ^ The window function -> v n windowedSinc size cutoff window = VG.zipWith (*) (sinc size cutoff) (window size) signal :: [Double] -> [Double] -> [(Double, Double)] signal coeffs xs = [ (x / pi, func x) | x <- xs ] where func phase = magnitude $ sum $ zipWith (\index mag -> mkPolar mag (phase * (- index))) (iterate (+ 1) (- ((fromIntegral (length coeffs) - 1) / 2))) coeffs -- | Given filter coefficients, plot their frequency response and save the graph as "frequency_response.png". plotFrequency :: [Double] -- ^ The filter coefficients -> IO () plotFrequency coeffs = toFile def "frequency_response.png" $ do layout_title .= "Frequency Response" plot (line "Frequency Response" [signal coeffs $ takeWhile (< pi) $ iterate (+ 0.01) 0]) --ts is really the ratio ts / sampling period -- | Square root raised cosine srrc :: (Ord a, Floating a) => Int -- ^ size: from [-n .. n] -> Int -- ^ sampling period -> a -- ^ beta -> [a] srrc n ts beta = map func [(-n) .. n] where func x | x == 0 = 1 - beta + 4 * beta / pi | abs (fromIntegral x) ~= (fromIntegral ts / (4 * beta)) = (beta / sqrt 2) * ((1 + 2/pi) * sin (pi / (4 * beta)) + (1 - 2/pi) * cos (pi / (4 * beta))) | otherwise = (sin (pi * xdivts * (1 - beta)) + 4 * beta * xdivts * cos (pi * xdivts * (1 + beta))) / (pi * xdivts * (1 - (4 * beta * xdivts) ** 2)) where xdivts = fromIntegral x / fromIntegral ts x ~= y = abs (x - y) < 0.001