Update fir post for filter type table and code examples

1 files changed, 64 insertions, 2 deletions

diff --git a/md/writeup/calculate_fir_coefficients_with_c.md b/md/writeup/calculate_fir_coefficients_with_c.md
index e364eb4..295fa3f 100644
--- a/md/writeup/calculate_fir_coefficients_with_c.md
+++ b/md/writeup/calculate_fir_coefficients_with_c.md
@@ -12,7 +12,8 @@ and was able to use them just from tools that take as input parameters and
 give as output coefficients. Now time came just to calculate FIR from ground up.
 Also C is perfect to do stuff without abstraction levels hiding details, and can
 be ported to other languages and platforms. Lets calculate filter coefficients
-with windows  method. There is few more but those for later.
+with windows  method. Theory is not explained, there is a lot of playlists 
+on youtube and lecture notes online to check on that.
 
 ## Implementation
 
@@ -29,7 +30,7 @@ MathJax = {
 </script>
 Low pass ideal impulse response
 
-Ideal impulse response of the filter
+Ideal impulse response for low-pass filter
 
 $$2f_c\frac{sin(n \omega_c)}{n \omega_c}$$
 
@@ -75,6 +76,64 @@ for (i=0;i<filter_N;i++) {
 How to use calculated coefficients 
 [/writeup/dsp_lp_filter.md#toc-6](/writeup/dsp_lp_filter.md#toc-6)
 
+## Ideal impulse response 
+
+| Filter type| Ideal impulse response | 
+|---|---|
+| Lowpass  | $2f_c\frac{sin(n \omega_c)}{n \omega_c}$ |
+| Highpass | $-2f_c\frac{sin(n \omega_c)}{n \omega_c}$ |
+| Bandpass | $2f_c\frac{sin(n \omega_2)}{n \omega_2}-2f_c\frac{sin(n \omega_1)}{n \omega_1}$ |
+| Bandstop | $2f_c\frac{sin(n \omega_1)}{n \omega_1}-2f_c\frac{sin(n \omega_2)}{n \omega_2}$ |
+
+### Lowpass
+
+```c
+for (i=0;i<filter_N;i++) {
+        arg = (double)i-(double)(filter_N-1)/2.0;
+        h[i] = omega_c * sinc(omega_c*arg*M_PI);
+}
+```
+
+### Highpass
+
+```c
+for (i=0;i<filter_N;i++) {
+    arg = (double)i-(double)(filter_N-1)/2.0;
+    if (arg == 0.0) {
+        h[i] = 0.0;
+    } else {
+    
+        h[i] = cos(omega_c*arg*M_PI)/M_PI/arg + cos(arg*M_PI);
+    }
+}
+```
+
+### Bandpass
+
+```c
+for (i=0;i<filter_N;i++) {
+        arg = (double)i-(double)(filter_N-1)/2.0;
+        if (arg==0.0) {
+            h[i] = 0.0;
+        } else {
+            h[i] = (cos(omega_c1*arg*M_PI) - cos(omega_c2*arg*M_PI))/M_PI/arg;
+        }
+    }
+```
+
+### Bandstop
+
+```c
+    for (i=0;i<filter_N;i++) {
+        arg = (double)i-(double)(filter_N-1)/2.0;
+        if (arg==0.0) {
+            h[i] = 0.0;
+        } else {
+            h[i] = sinc(arg*M_PI)  - omega_c2*sinc(omega_c2*arg*M_PI) - omega_c1*sinc(omega_c1*arg*M_PI);
+        }
+    }
+```
+
 ## Windowing methods
 
 Here is most common windows for window methods that can give you better results then naive rectangular windows filter.
@@ -253,3 +312,6 @@ https://ccrma.stanford.edu/~jos/st/FFT_Simple_Sinusoid.html
 https://ccrma.stanford.edu/~jos/st/Example_Applications_DFT.html  
 https://ccrma.stanford.edu/~jos/st/Use_Blackman_Window.html  
 http://www.iowahills.com/A7ExampleCodePage.html  
+Digital Signal Processing: A Practical Approach by (Emmanuel Ifeachor, Barrie Jervis)  
+
+