Add --precise to compensate for audio start being truncated to sample

The starting time for  audio read for a pixel column is truncated to an
integer (a sample number) which introduces a semi-random time jitter of
up to one sample period and making the actual start time up to one sample
period earlier than requested. This patch tries to compensate for that by
linear interpolation between each sample and the following one.

src/spectrogram.c

@@ -34,6 +34,7 @@
 #include <stdbool.h>
 #include <math.h>
 #include <limits.h>
+#include <assert.h>
 
 #include <cairo.h>
 #include <fftw3.h>
@@ -65,6 +66,11 @@ typedef struct
 	double spec_floor_db ;
 } RENDER ;
 
+/* Interpolate between samples to eliminate the
+ * 1-sample-period jitter due to time quantization?
+ */
+static bool precise_timing = 0;
+
 typedef struct
 {	int left, top, width, height ;
 } RECT ;
@@ -157,11 +163,17 @@ static void
 read_mono_audio (SNDFILE * file, sf_count_t filelen, double * data, int datalen, int indx, int total)
 {
 	sf_count_t start ;
+	double error ;	 /* How much "start" is wrong by
+			  * (start == exact_value_of_start + error) */
+	sf_count_t k;
 
 	memset (data, 0, datalen * sizeof (data [0])) ;
 
 	start = (indx * filelen) / total - datalen / 2 ;
 
+	error = start - (((double)indx * filelen) / total - datalen / 2.0) ;
+	assert (-1.0 < error && error <= 0.0) ;
+
 	if (start >= 0)
 		sf_seek (file, start, SEEK_SET) ;
 	else
@@ -171,7 +183,23 @@ read_mono_audio (SNDFILE * file, sf_count_t filelen, double * data, int datalen,
 		datalen -= start ;
 		} ;
 
-	sfx_mix_mono_read_double (file, data, datalen) ;
+	sfx_mix_mono_read_double (file, data, datalen+(precise_timing?1:0)) ;
+
+	/* The starting time is truncated to a sample boundary and is slighty
+	 * earlier that the exact starting time.
+	 * We compensate by reading in one more sample than this and
+	 * interpolating between each sample and the following one.
+	 */
+	if ( precise_timing && error != 0.0 )
+	{
+		/* Proportion to take of this sample and of the following one.
+		 * this + next == 1.0
+		 */
+		double this = 1.0 + error, next = -error ;
+
+		for (k=0; k < datalen; k++)
+			data[k] = data[k]*this + data[k+1]*next;
+	}
 
 	return ;
 } /* read_mono_audio */
@@ -589,7 +617,9 @@ render_to_surface (const RENDER * render, SNDFILE *infile, int samplerate, sf_co
 			}
 		}
 
-	time_domain		= calloc (2 * speclen, sizeof (double)) ;
+	/* + 1 because with --precise, read_mono_audio reads the following
+	 * sample and interpolates to get the starting moment exact. */
+	time_domain		= calloc ((2 * speclen + 1), sizeof (double)) ;
 	freq_domain		= calloc (2 * speclen, sizeof (double)) ;
 	single_mag_spec = calloc (speclen, sizeof (double)) ;
 	mag_spec		= calloc (width, sizeof (float *)) ;
@@ -738,6 +768,7 @@ usage_exit (const char * argv0, int error)
 		"        --kaiser               : Use a Kaiser window function (the default)\n"
 		"        --nuttall              : Use a Nuttall window function\n"
 		"        --hann                 : Use a Hann window function\n"
+		"        --precise              : Interpolate between samples for precise timing\n"
 		) ;
 
 	exit (error) ;
@@ -795,6 +826,11 @@ main (int argc, char * argv [])
 			continue ;
 			} ;
 
+		if (strcmp (argv [k], "--precise") == 0)
+		{	precise_timing = 1;
+			continue ;
+			} ;
+
 		printf ("\nError : Bad command line argument '%s'\n", argv [k]) ;
 		usage_exit (argv [0], 1) ;
 		} ;