feat(dsp): add/update power & integral fns

packages/dsp/src/fft/power.ts

@@ -1,34 +1,78 @@
 import type { NumericArray } from "@thi.ng/api";
+import { isNumber } from "@thi.ng/checks";
 import type { ComplexArray } from "../api";
 import { isComplex } from "../util/complex";
 
 /**
- * Computes the `sum(f(i)^2)` for given array.
+ * Computes the sum of the given array.
  *
  * @param window
  */
 export const integralT = (window: NumericArray) => {
     let sum = 0;
     for (let i = window.length; --i >= 0; ) {
-        // prettier-ignore
-        sum += (<number>window[i]) ** 2;
+        sum += window[i];
     }
     return sum;
 };
 
 /**
- * Computes the `sum(|c(i)|^2)` for given complex array.
+ * Computes the squared sum of given array.
+ *
+ * @param window
+ */
+export const integralTSquared = (window: NumericArray) => {
+    let sum = 0;
+    for (let i = window.length; --i >= 0; ) {
+        sum += window[i] ** 2;
+    }
+    return sum;
+};
+
+/**
+ * Computes the `sum(|c(i)|)` for given complex array.
  *
  * @param window
  */
 export const integralF = ([real, img]: ComplexArray) => {
+    let sum = 0;
+    for (let i = real.length; --i >= 0; ) {
+        sum += Math.hypot(real[i], img[i]);
+    }
+    return sum;
+};
+
+/**
+ * Computes the `sum(|c(i)|^2)` for given complex array.
+ *
+ * @param window
+ */
+export const integralFSquared = ([real, img]: ComplexArray) => {
     let sum = 0;
     for (let i = real.length; --i >= 0; ) {
         sum += real[i] ** 2 + img[i] ** 2;
     }
     return sum;
 };
 
+/**
+ * If `scale` is a number, returns it. Else returns `base / integralT(scale)`.
+ *
+ * @param scale
+ * @param base
+ */
+export const powerScale = (scale: number | NumericArray, base = 1) =>
+    isNumber(scale) ? scale : base / integralT(scale);
+
+/**
+ * If `scale` is a number, returns it. Else returns `integralT(scale) / base`.
+ *
+ * @param scale
+ * @param base
+ */
+export const invPowerScale = (scale: number | NumericArray, base = 1) =>
+    isNumber(scale) ? scale : integralT(scale) / base;
+
 /**
  * Computes sum squared power of given time or frequency domain window.
  *
@@ -41,8 +85,8 @@ export const integralF = ([real, img]: ComplexArray) => {
  */
 export const powerSumSquared = (window: NumericArray | ComplexArray) =>
     isComplex(window)
-        ? integralF(window) / window[0].length
-        : integralT(window);
+        ? integralFSquared(window) / window[0].length
+        : integralTSquared(window);
 
 /**
  * Computes mean squared power of given time or frequency domain window.
@@ -72,4 +116,6 @@ export const powerMeanSquared = (window: NumericArray | ComplexArray) =>
 export const powerTimeIntegral = (
     window: NumericArray | ComplexArray,
     fs: number
-) => (isComplex(window) ? integralF(window) : integralT(window)) / fs;
+) =>
+    (isComplex(window) ? integralFSquared(window) : integralTSquared(window)) /
+    fs;