Unified · Split
| @@ -4,7 +4,10 @@ · 3 unmodified lines | ||
| 4 | 4 | \overfullrule 0pt |
| 5 | 5 | \noindent |
| 6 | 6 | $$ |
| 7 | −y(n) = \alpha x(n) + \beta(1 + \alpha)x(n - 1) + x(n - 2) | |
| 8 | −- \beta(1 + \alpha)z^{-1} y(n - 1) - \alpha y(n - 2) | |
| 7 | +\eqalign { | |
| 8 | +y(n) = &\alpha x(n) + \beta(1 + \alpha)x(n - 1) + x(n - 2) | |
| 9 | +\cr | |
| 10 | +- &\beta(1 + \alpha)y(n - 1) - \alpha y(n - 2) | |
| 11 | +} | |
| 9 | 12 | $$ |
| 10 | 13 | \bye |
| @@ -4,7 +4,10 @@ · 3 unmodified lines | ||
| 4 | 4 | \overfullrule 0pt |
| 5 | 5 | \noindent |
| 6 | 6 | $$ |
| 7 | −v(n) = x(n) - \beta(1 + \alpha)v(n - 1) - \alpha v(n - 2) | |
| 8 | −y(n) = \alpha v(n) + \beta(1 + \alpha) v(n - 1) + v(n - 2) | |
| 7 | +\eqalign{ | |
| 8 | +v(n) &= x(n) - \beta(1 + \alpha)v(n - 1) - \alpha v(n - 2) | |
| 9 | +\cr | |
| 10 | +y(n) &= \alpha v(n) + \beta(1 + \alpha) v(n - 1) + v(n - 2) | |
| 11 | +} | |
| 9 | 12 | $$ |
| 10 | 13 | \bye |
| @@ -4,7 +4,9 @@ · 3 unmodified lines | ||
| 4 | 4 | \overfullrule 0pt |
| 5 | 5 | \noindent |
| 6 | 6 | $$ |
| 7 | −v(n) = x(n) - a_1 v(n - 1) - a_2 v(n - 2) | |
| 8 | −y(n) = b_0 v(n) + b_1 v(n - 1) + b_2 v(n - 2) | |
| 7 | +\eqalign{ | |
| 8 | +v(n) &= x(n) - a_1 v(n - 1) - a_2 v(n - 2) \cr | |
| 9 | +y(n) &= b_0 v(n) + b_1 v(n - 1) + b_2 v(n - 2) | |
| 10 | +} | |
| 9 | 11 | $$ |
| 10 | 12 | \bye |
| @@ -34,8 +34,11 @@ This has the following difference equation: · 33 unmodified lines | ||
| 34 | 34 | @! |
| 35 | 35 | (fig "peakeq_df1_difference" |
| 36 | 36 | `` |
| 37 | −y(n) = \alpha x(n) + \beta(1 + \alpha)x(n - 1) + x(n - 2) | |
| 38 | −- \beta(1 + \alpha)z^{-1} y(n - 1) - \alpha y(n - 2) | |
| 37 | +\eqalign { | |
| 38 | +y(n) = &\alpha x(n) + \beta(1 + \alpha)x(n - 1) + x(n - 2) | |
| 39 | +\cr | |
| 40 | +- &\beta(1 + \alpha)y(n - 1) - \alpha y(n - 2) | |
| 41 | +} | |
| 39 | 42 | ``) |
| 40 | 43 | !@ |
| 41 | 44 | |
| @@ -45,8 +48,10 @@ represented in this generalized difference equation: · 3 unmodified lines | ||
| 45 | 48 | |
| 46 | 49 | @!(fig "peakeq_df2_structure" |
| 47 | 50 | `` |
| 48 | −v(n) = x(n) - a_1 v(n - 1) - a_2 v(n - 2) | |
| 49 | −y(n) = b_0 v(n) + b_1 v(n - 1) + b_2 v(n - 2) | |
| 51 | +\eqalign{ | |
| 52 | +v(n) &= x(n) - a_1 v(n - 1) - a_2 v(n - 2) \cr | |
| 53 | +y(n) &= b_0 v(n) + b_1 v(n - 1) + b_2 v(n - 2) | |
| 54 | +} | |
| 50 | 55 | ``)!@ |
| 51 | 56 | |
| 52 | 57 | Converting to direct form II is a matter of putting |
| @@ -56,8 +61,11 @@ following difference equation: · 3 unmodified lines | ||
| 56 | 61 | |
| 57 | 62 | @!(fig "peakeq_df2_difference" |
| 58 | 63 | `` |
| 59 | −v(n) = x(n) - \beta(1 + \alpha)v(n - 1) - \alpha v(n - 2) | |
| 60 | −y(n) = \alpha v(n) + \beta(1 + \alpha) v(n - 1) + v(n - 2) | |
| 64 | +\eqalign{ | |
| 65 | +v(n) &= x(n) - \beta(1 + \alpha)v(n - 1) - \alpha v(n - 2) | |
| 66 | +\cr | |
| 67 | +y(n) &= \alpha v(n) + \beta(1 + \alpha) v(n - 1) + v(n - 2) | |
| 68 | +} | |
| 61 | 69 | `` |
| 62 | 70 | )!@ |
| 63 | 71 | |