Aufgaben:Exercise 4.11: C Program "acf1" - Revision history

Guenter at 15:28, 28 April 2022

2022-04-28T15:28:39Z

Guenter at 16:39, 31 March 2022

2022-03-31T16:39:04Z

Guenter at 15:53, 21 March 2022

2022-03-21T15:53:01Z

Guenter at 15:47, 21 March 2022

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Guenter at 15:39, 21 March 2022

2022-03-21T15:39:41Z

Noah at 12:43, 6 March 2022

2022-03-06T12:43:07Z

Noah at 15:25, 4 March 2022

2022-03-04T15:25:07Z

Noah at 00:00, 1 March 2022

2022-03-01T00:00:27Z

Noah at 00:00, 1 March 2022

2022-03-01T00:00:04Z

Noah at 23:59, 28 February 2022

2022-02-28T23:59:48Z

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Sto_A_4_11.png|right|frame|C program&nbsp; $1$&nbsp; for the ACF calculation '''correction''']]
+[[File:EN_Sto_A_4_11_neu2.png|right|frame|C program&nbsp; $1$&nbsp; for the ACF calculation]]
 See the C&ndash;program "acf1" for calculating the discrete ACF values&nbsp; $\varphi_x(k)$&nbsp; with index&nbsp; $k = 0$, ... , $l$.&nbsp; The following should be noted about this:

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID391__Sto_A_4_11.png|right|frame|C program&nbsp; $1$&nbsp; for the ACF calculation '''correction''']]
+[[File:EN_Sto_A_4_11.png|right|frame|C program&nbsp; $1$&nbsp; for the ACF calculation '''correction''']]
 See the C&ndash;program "acf1" for calculating the discrete ACF values&nbsp; $\varphi_x(k)$&nbsp; with index&nbsp; $k = 0$, ... , $l$.&nbsp; The following should be noted about this:

@@ Line 32: / Line 32: @@
 <quiz display=simple>
-{Which elements&nbsp; $i$&nbsp; and&nbsp; $j$&nbsp; of the auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; are used <u>on the first loop pass</u>&nbsp; $(z=0)$&nbsp; to calculate the ACF&ndash;value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values&nbsp; $x_\nu$&nbsp; are in these memory cells?
+{Which elements&nbsp; $i$&nbsp; and&nbsp; $j$&nbsp; of the auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; are used&nbsp; <u>on the first loop pass</u> &nbsp; $(z=0)$&nbsp; to calculate the ACF&ndash;value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values&nbsp; $x_\nu$&nbsp; are in these memory cells?
 |type="{}"}
 $i \ = \ $ { 0. }
@@ Line 38: / Line 38: @@
-{Which memory cell&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm} \big]$&nbsp; will be occupied <u>after the first loop pass</u>&nbsp; $(z=0)$&nbsp; with a new random variable&nbsp; $x_\nu$&nbsp;? <br> Which index &nbsp; $\nu$&nbsp; is entered in the process?
+{Which memory cell&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm} \big]$&nbsp; will be occupied&nbsp; <u>after the first loop pass</u> &nbsp; $(z=0)$&nbsp; with a new random variable&nbsp; $x_\nu$&nbsp;? <br> Which index &nbsp; $\nu$&nbsp; is entered in the process?
 |type="{}"}
 $i \ = \ $   { 0. }

@@ Line 56: / Line 56: @@
 ===Solution===
 {{ML-Kopf}}
-[[File:P_ID417__Sto_A_4_11_b.png|right|frame|For numerical ACF calculation]]
+[[File:P_ID417__Sto_A_4_11_b.png|right|frame|For the exemplary numerical ACF calculation]]
 <br>
 '''(1)'''&nbsp; With&nbsp; $z= 0$&nbsp; and&nbsp; $k=6$&nbsp; results according to the program: &nbsp; $\underline{i= 0}$&nbsp; and&nbsp; $\underline{j= 6}$.
@@ Line 71: / Line 71: @@
 '''(3)'''&nbsp; The graph shows the allocation of the auxiliary field with the random values&nbsp; $x_\nu$.
-*In each case, the memory cell is highlighted in green&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm}\big]$.&nbsp; The new random variable is entered into this memory location at the end of each loop (line 18).
+*In each case,&nbsp; the memory cell&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm}\big]$&nbsp; is highlighted in green.&nbsp; The new random variable is entered into this memory location at the end of each loop&nbsp; (line 18).
-*For&nbsp; $z= 83$&nbsp; and&nbsp; $K=6$&nbsp; this results in.
+*For&nbsp; $z= 83$&nbsp; and&nbsp; $K=6$&nbsp; this results in
 :$$\underline{i= 83 \hspace{-0.2cm}\mod \hspace{-0.15cm} \ 11 = 6},\hspace{1cm} \underline{j= (i+k)\hspace{-0.2cm}\mod \hspace{-0.15cm} \ 11 = 1}.$$
 *Loop pass&nbsp; $z= 83$: &nbsp; In memory cell&nbsp; ${\rm H}\big[\hspace{0.03cm} 6 \hspace{0.03cm}\big]$&nbsp; is the random variable&nbsp; $x_{84}$&nbsp; and in the memory cell&nbsp; ${\rm H}\big[\hspace{0.03cm} 1 \hspace{0.03cm}\big]$&nbsp; is the random variable&nbsp; $x_{90}$.
-*At the end of the loop pass&nbsp; $z= 83$&nbsp; in&nbsp; ${\rm H}\big[\hspace{0.03cm} 6 \hspace{0.03cm}\big]$&nbsp; the content&nbsp; $x_{84}$&nbsp; is replaced by&nbsp; $x_{95}$&nbsp;.
+*At the end of loop pass&nbsp; $z= 83$&nbsp; in&nbsp; ${\rm H}\big[\hspace{0.03cm} 6 \hspace{0.03cm}\big]$:&nbsp; The content&nbsp; $x_{84}$&nbsp; is replaced by&nbsp; $x_{95}$&nbsp;.
 {{ML-Fuß}}

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID391__Sto_A_4_11.png|right|frame|C program&nbsp; $1$&nbsp; for ACF&ndash;calculation '''correction''']]
+[[File:P_ID391__Sto_A_4_11.png|right|frame|C program&nbsp; $1$&nbsp; for the ACF calculation '''correction''']]
 See the C&ndash;program "acf1" for calculating the discrete ACF values&nbsp; $\varphi_x(k)$&nbsp; with index&nbsp; $k = 0$, ... , $l$.&nbsp; The following should be noted about this:
-* Let the long&ndash;value passed to the program&nbsp; $l = 10$.&nbsp; The ACF values&nbsp; $\varphi_x(0)$, ... , $\varphi_x(10)$&nbsp; are returned to the calling program with the float field&nbsp; $\rm ACF\big[ \ \big]$&nbsp; . In lines 7 and 8 of the program given on the right, this field is pre-populated with zeros.
+* The long&ndash;value passed to the program is&nbsp; $l = 10$.&nbsp; The ACF values&nbsp; $\varphi_x(0)$, ... , $\varphi_x(10)$&nbsp; are returned to the calling program with the float field&nbsp; $\rm ACF\big[ \ \big]$.&nbsp;  In lines 7 and 8 of the program given on the right,&nbsp; this field is pre-populated with zeros.
-* The random variables to be analyzed&nbsp; $x_\nu$&nbsp; are generated with the float function&nbsp; $x( \ )$&nbsp; (see line 4).&nbsp; This function is called a total of&nbsp; $N + l + 1 = 10011$&nbsp; times (lines 9 and 18).
+* The random variables&nbsp; $x_\nu$&nbsp; to be analyzed are generated with the float function&nbsp; $x( \ )$,&nbsp; see line 4.&nbsp; This function is called a total of&nbsp; $N + l + 1 = 10011$&nbsp; times&nbsp; $x_\nu$&nbsp; (lines 9 and 18).
-* In contrast to the algorithm given in the&nbsp; [[Theory_of_Stochastic_Signals/Auto-Correlation_Function#Numerical_ACF_determination|Theory section]]&nbsp; program&nbsp; "acf2"&nbsp; of&nbsp; [[Aufgaben:Exercise_4.11Z:_C_Program_"acf2"|Task 4.11Z]]&nbsp; directly implemented, one needs here an auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; with only&nbsp; $l + 1 = 11$&nbsp; memory elements.
+* In contrast to the algorithm given in the&nbsp; [[Theory_of_Stochastic_Signals/Auto-Correlation_Function#Numerical_ACF_determination|Theory section]]&nbsp; directly implemented in the program&nbsp; "acf2"&nbsp; of&nbsp; [[Aufgaben:Exercise_4.11Z:_C_Program_"acf2"|Task 4.11Z]],&nbsp; one needs here an auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; with only&nbsp; $l + 1 = 11$&nbsp; memory elements.
-* Before starting the actual calculation algorithm (lines 11 to 21), the eleven memory cells of&nbsp; ${\rm H}\big[ \ \big]$&nbsp; contain the random values&nbsp; $x_1$, ... ,&nbsp; $x_{11}$.
+* Finally,&nbsp; in lines 22 and 23,&nbsp; all ACF values are divided by the number&nbsp; $N$&nbsp; of analyzed  data.
@@ Line 34: / Line 32: @@
 <quiz display=simple>
-{Which elements&nbsp; $i$&nbsp; and&nbsp; $j$&nbsp; of the auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; are used <u>on the first pass</u>&nbsp; $(z=0)$&nbsp; to calculate the ACF&ndash;value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values&nbsp; $x_\nu$&nbsp; are in these memory cells?
+{Which elements&nbsp; $i$&nbsp; and&nbsp; $j$&nbsp; of the auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; are used <u>on the first loop pass</u>&nbsp; $(z=0)$&nbsp; to calculate the ACF&ndash;value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values&nbsp; $x_\nu$&nbsp; are in these memory cells?
 |type="{}"}
 $i \ = \ $ { 0. }

@@ Line 14: / Line 14: @@
 * Before starting the actual calculation algorithm (lines 11 to 21), the eleven memory cells of&nbsp; ${\rm H}\big[ \ \big]$&nbsp; contain the random values&nbsp; $x_1$, ... ,&nbsp; $x_{11}$.
-*The outer loop with the run variable&nbsp; $z$&nbsp; (marked in red) is run&nbsp; $N$ times.
+*The outer loop with the index&nbsp; $z$&nbsp; (marked in red) is run&nbsp; $N$ times.
 *In the inner loop&nbsp; (marked white)&nbsp; with the index&nbsp; $k = 0$, ... ,&nbsp; $l$&nbsp; all memory cells of the field&nbsp; ${\rm ACF}\big[\hspace{0.03cm} k \hspace{0.03cm} \big]$&nbsp; are increased by the contribution&nbsp; $x_\nu \cdot x_{\nu+k}$&nbsp;.

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID391__Sto_A_4_11.png|right|frame|C program&nbsp; $1$&nbsp; for AKF&ndash;calculation '''correction''']]
+[[File:P_ID391__Sto_A_4_11.png|right|frame|C program&nbsp; $1$&nbsp; for ACF&ndash;calculation '''correction''']]
-See the C&ndash;program "akf1" for calculating the discrete AKF values&nbsp; $\varphi_x(k)$&nbsp; with index&nbsp; $k = 0$, ... , $l$.&nbsp; The following should be noted about this:
+See the C&ndash;program "akf1" for calculating the discrete ACF values&nbsp; $\varphi_x(k)$&nbsp; with index&nbsp; $k = 0$, ... , $l$.&nbsp; The following should be noted about this:
-* Let the long&ndash;value passed to the program&nbsp; $l = 10$.&nbsp; The AKF values&nbsp; $\varphi_x(0)$, ... , $\varphi_x(10)$&nbsp; are returned to the calling program with the float field&nbsp; $\rm AKF\big[ \ \big]$&nbsp; . In lines 7 and 8 of the program given on the right, this field is pre-populated with zeros.
+* Let the long&ndash;value passed to the program&nbsp; $l = 10$.&nbsp; The ACF values&nbsp; $\varphi_x(0)$, ... , $\varphi_x(10)$&nbsp; are returned to the calling program with the float field&nbsp; $\rm ACF\big[ \ \big]$&nbsp; . In lines 7 and 8 of the program given on the right, this field is pre-populated with zeros.
 * The random variables to be analyzed&nbsp; $x_\nu$&nbsp; are generated with the float function&nbsp; $x( \ )$&nbsp; (see line 4).&nbsp; This function is called a total of&nbsp; $N + l + 1 = 10011$&nbsp; times (lines 9 and 18).
-* In contrast to the algorithm given in the&nbsp; [[Theory_of_Stochastic_Signals/Auto-Correlation_Function#Numerical_ACF_determinationTheory section]]&nbsp; program&nbsp; "akf2"&nbsp; of&nbsp; [[Aufgaben:Exercise_4.11Z:_C_Program_"acf2"|Task 4.11Z]]&nbsp; directly implemented, one needs here an auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; with only&nbsp; $l + 1 = 11$&nbsp; memory elements.
+* In contrast to the algorithm given in the&nbsp; [[Theory_of_Stochastic_Signals/Auto-Correlation_Function#Numerical_ACF_determination|Theory section]]&nbsp; program&nbsp; "akf2"&nbsp; of&nbsp; [[Aufgaben:Exercise_4.11Z:_C_Program_"acf2"|Task 4.11Z]]&nbsp; directly implemented, one needs here an auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; with only&nbsp; $l + 1 = 11$&nbsp; memory elements.
 * Before starting the actual calculation algorithm (lines 11 to 21), the eleven memory cells of&nbsp; ${\rm H}\big[ \ \big]$&nbsp; contain the random values&nbsp; $x_1$, ... ,&nbsp; $x_{11}$.
 *The outer loop with the run variable&nbsp; $z$&nbsp; (marked in red) is run&nbsp; $N$ times.
-*In the inner loop&nbsp; (marked white)&nbsp; with the run index&nbsp; $k = 0$, ... ,&nbsp; $l$&nbsp; all memory cells of the field&nbsp; ${\rm AKF}\big[\hspace{0.03cm} k \hspace{0.03cm} \big]$&nbsp; are increased by the contribution&nbsp; $x_\nu \cdot x_{\nu+k}$&nbsp;.
+*In the inner loop&nbsp; (marked white)&nbsp; with the run index&nbsp; $k = 0$, ... ,&nbsp; $l$&nbsp; all memory cells of the field&nbsp; ${\rm ACF}\big[\hspace{0.03cm} k \hspace{0.03cm} \big]$&nbsp; are increased by the contribution&nbsp; $x_\nu \cdot x_{\nu+k}$&nbsp;.
-* Finally, in lines 22 and 23, all AKF&ndash;values are divided by the number&nbsp; $N$&nbsp; of data analyzed.
+* Finally, in lines 22 and 23, all ACF&ndash;values are divided by the number&nbsp; $N$&nbsp; of data analyzed.
@@ Line 26: / Line 25: @@
 Hint:
-*Die Aufgabe gehört zum  Kapitel&nbsp; [[Theory_of_Stochastic_Signals/Auto-Correlation_Function|Auto-Correlation Function]].
+*This exercise belongs to the chapter&nbsp; [[Theory_of_Stochastic_Signals/Auto-Correlation_Function|Auto-Correlation Function]].
 *Reference is made in particular to the page&nbsp; [[Theory_of_Stochastic_Signals/Auto-Correlation_Function#Numerical_ACF_determination|Numerical ACF determination]].
@@ Line 35: / Line 34: @@
 <quiz display=simple>
-{Which elements&nbsp; $i$&nbsp; and&nbsp; $j$&nbsp; of the auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; are used <u>on the first pass</u>&nbsp; $(z=0)$&nbsp; to calculate the AKF&ndash;value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values&nbsp; $x_\nu$&nbsp; are in these memory cells?
+{Which elements&nbsp; $i$&nbsp; and&nbsp; $j$&nbsp; of the auxiliary field&nbsp; ${\rm H}\big[ \ \big]$&nbsp; are used <u>on the first pass</u>&nbsp; $(z=0)$&nbsp; to calculate the ACF&ndash;value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values&nbsp; $x_\nu$&nbsp; are in these memory cells?
 |type="{}"}
 $i \ = \ $ { 0. }
@@ Line 41: / Line 40: @@
-{Which memory cell&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm} \big]$&nbsp; will be occupied <u>after the first loop pass</u>&nbsp; $(z=0)$&nbsp; with a new random variable&nbsp; $x_\nu$&nbsp;?
+{Which memory cell&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm} \big]$&nbsp; will be occupied <u>after the first loop pass</u>&nbsp; $(z=0)$&nbsp; with a new random variable&nbsp; $x_\nu$&nbsp;? <br> Which index &nbsp; $\nu$&nbsp; is entered in the process?
-{Welche Speicherelemente&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm} \big]$&nbsp; und&nbsp; ${\rm H}\big[\hspace{0.03cm} j \hspace{0. 03cm} \big]$&nbsp; are used in the loop pass&nbsp; $z=83$&nbsp; to calculate the AKF value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values are in these memory cells?
+{Which memory elements&nbsp; ${\rm H}\big[\hspace{0.03cm} i \hspace{0.03cm} \big]$&nbsp; and&nbsp; ${\rm H}\big[\hspace{0.03cm} j \hspace{0.03cm} \big]$&nbsp; are used in the loop pass&nbsp; $z=83$&nbsp; to calculate the ACF value&nbsp; $\varphi(k=6)$&nbsp;? <br>What random values are in these memory cells?
 |type="{}"}
-$i \ = \ $ { 6 }
+$i \ = \ $   { 6 }
 $j \ = \ $ { 1 }
@@ Line 56: / Line 58: @@
 ===Solution===
 {{ML-Kopf}}
-[[File:P_ID417__Sto_A_4_11_b.png|right|frame|For numerical AKF calculation]]
+[[File:P_ID417__Sto_A_4_11_b.png|right|frame|For numerical ACF calculation]]
 <br>
 '''(1)'''&nbsp; With&nbsp; $z= 0$&nbsp; and&nbsp; $k=6$&nbsp; results according to the program: &nbsp; $\underline{i= 0}$&nbsp; and&nbsp; $\underline{j= 6}$.