Update analysis example #7

.gitignore

@@ -18,3 +18,5 @@ Thumbs.db
 
 test.*.dft
 test.*.wav
+
+*.npy

rust/Cargo.toml

@@ -14,3 +14,5 @@ categories = ["algorithms", "mathematics", "multimedia", "science"]
 num = "*"
 
 [dev-dependencies]
+ndarray = "0.15.*"
+ndarray-npy = "0.8.*"

rust/Makefile

@@ -13,6 +13,7 @@ clean:
 example:
 	@cargo build --examples
 	@cargo run --example analysis
+	@python examples/analysis.py
 
 test:
 	@cargo build --tests

rust/examples/analysis.py

@@ -0,0 +1,35 @@
+import matplotlib.pyplot as plot
+import numpy as np
+import os
+
+npy = os.path.join("examples", "analysis.npy")
+dft = np.load(npy)
+
+sr = 44100
+n = len(dft)
+
+with np.errstate(all='ignore'):
+    db = 20 * np.log10(np.abs(dft))
+
+roi = (0, n / sr, 0, 1)
+
+args = dict(extent=roi,
+            origin='lower',
+            aspect='auto',
+            cmap='inferno',
+            interpolation='nearest')
+
+plot.imshow(db.T, **args)
+cbar = plot.colorbar()
+
+plot.xlabel('s')
+plot.ylabel('Hz')
+cbar.set_label('dB')
+
+plot.clim(-120, 0)
+
+# freqs = qdft.frequencies
+# ticks = np.linspace(0, 1, freqs.size, endpoint=True)
+# plot.gca().yaxis.set_major_formatter(lambda tick, _: np.interp(tick, ticks, freqs).astype(int))
+
+plot.show()

rust/examples/analysis.rs

@@ -1,7 +1,26 @@
-use num::Zero;
-use num::complex::Complex;
 use qdft::QDFT;
 
+use ndarray::Array1 as Vector;
+use ndarray::Array2 as Matrix;
+use ndarray_npy::write_npy;
+
+#[allow(non_camel_case_types)]
+type c64 = num::complex::Complex<f64>;
+
+fn phase(t: &Vector<f64>, f: &Vector<f64>) -> Vector<f64>
+{
+    let pi = std::f64::consts::PI;
+    let mut cs = Vector::<f64>::zeros(t.len());
+
+    for i in 1 .. t.len() {
+        let dt = t[i] - t[i - 1];
+        let dp = 2.0 * pi * f[i] * dt;
+        cs[i] = dp + cs[i - 1];
+    }
+
+  return cs;
+}
+
 fn main() {
     let samplerate = 44100.0;
     let bandwidth = (50.0, samplerate / 2.0);
@@ -16,12 +35,19 @@ fn main() {
         latency,
         window);
 
-    let n = 1;
-    let m = n * qdft.size();
+    let n = 1 * samplerate as usize;
+    let m = qdft.size();
+
+    let t = Vector::<f64>::range(0.0, n as f64, 1.0) / samplerate;
+    let f = Vector::<f64>::ones(n) * 1000.0;
+
+    let x = phase(&t, &f).mapv_into(|v|v.sin());
+    let mut y = Matrix::<c64>::zeros((n, m));
+
+    qdft.qdft(x.as_slice().unwrap(), y.as_slice_mut().unwrap());
 
-    let mut samples = vec![f32::zero(); n];
-    let mut dfts = vec![Complex::<f64>::zero(); m];
+    let npy = std::path::Path::new("examples").join("analysis.npy");
+    let error = format!("Unable to create {}!", npy.to_str().unwrap());
 
-    qdft.qdft(&samples, &mut dfts);
-    qdft.iqdft(&dfts, &mut samples);
+    write_npy(npy, &y).expect(error.as_str());
 }

rust/src/lib.rs

@@ -1,7 +1,6 @@
 #![allow(unused)]
 
-use num::Float;
-use num::Zero;
+use num::{Float, Zero};
 use num::complex::Complex;
 use std::collections::VecDeque;
 
@@ -278,6 +277,6 @@ mod tests {
         }
 
         assert_eq!(i, qdft.size);
-        assert_eq!(j, (qdft.size as isize) * 3 + 1);
+        assert_eq!(j, (qdft.size * 3 + 1) as isize);
     }
 }

rust/tests/test.rs

@@ -1,11 +1,13 @@
 #[cfg(test)]
 mod tests {
 
-    use num::One;
-    use num::Zero;
-    use num::complex::Complex;
     use qdft::QDFT;
 
+    use num::{One, Zero};
+
+    #[allow(non_camel_case_types)]
+    type c64 = num::complex::Complex<f64>;
+
     #[test]
     fn test_one_in_zero_out() {
         let samplerate = 44100.0;
@@ -22,16 +24,16 @@ mod tests {
             window);
 
         let n = 1;
-        let m = n * qdft.size();
+        let m = qdft.size();
 
         let mut samples = vec![f32::zero(); n];
-        let mut dfts = vec![Complex::<f64>::zero(); m];
+        let mut dfts = vec![c64::zero(); n * m];
 
-        dfts[0] = Complex::one();
-        assert_ne!(dfts[0], Complex::zero());
+        dfts[0] = c64::one();
+        assert_ne!(dfts[0], c64::zero());
 
         qdft.qdft(&samples, &mut dfts);
-        assert_eq!(dfts[0], Complex::zero());
+        assert_eq!(dfts[0], c64::zero());
 
         samples[0] = f32::one();
         assert_ne!(samples[0], f32::zero());